Allemaal Getallen Index 0104

$104\mathbf{\color{blue}{\;=\;}}2+3+4+5+6+7+8+9+10+11+12+13+14$ (som van opeenvolgende gehele getallen)

$104\mathbf{\color{blue}{\;=\;}}6+8+10+12+14+16+18+20$ (som van opeenvolgende pare getallen)

$104\mathbf{\color{blue}{\;=\;}}23+25+27+29\mathbf{\color{blue}{\;=\;}}51+53$ (som van opeenvolgende onpare getallen)

$104\mathbf{\color{blue}{\;=\;}}((0;0;2;10)\,(0;2;6;8)\,(4;4;6;6))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#3\}$

$104\mathbf{\color{blue}{\;=\;}}((0;0;0;2;2;2;2;2;4)\,(0;1;1;1;1;1;2;3;4))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#2\}$

$104\mathbf{\color{blue}{\;=\;}}4!+4^2+4^3$

$104\mathbf{\color{blue}{\;=\;}}13*2^3\mathbf{\color{blue}{\;=\;}}(13-2^3)^3-13-2^3$

$104\mathbf{\color{blue}{\;=\;}}(1^2+1^2)*(4^2+6^2)\mathbf{\color{blue}{\;=\;}}(2^2+2^2)*(2^2+3^2)$

$104\mathbf{\color{blue}{\;=\;}}eulerphi(159,212,318)$

$104\mathbf{\color{blue}{\;=\;}}fibonacci_{(0,8)}[8]\mathbf{\color{blue}{\;=\;}}40+64$

$104\mathbf{\color{blue}{\;=\;}}tribonacci_{(0,0,8)}[8]\mathbf{\color{blue}{\;=\;}}16+32+56$

$104\mathbf{\color{blue}{\;=\;}}tetranacci_{(0,0,1,6)}[9]\mathbf{\color{blue}{\;=\;}}7+14+28+55$

$104\mathbf{\color{blue}{\;=\;}}2^2+10^2\mathbf{\color{blue}{\;=\;}}[3^6][9^3][27^2]-[5^4][25^2]\mathbf{\color{blue}{\;=\;}}[9^3][27^2]-25^2\mathbf{\color{blue}{\;=\;}}15^2-11^2\mathbf{\color{blue}{\;=\;}}30^3-164^2\mathbf{\color{blue}{\;=\;}}42^3-272^2$

104.1

$104\mathbf{\color{blue}{\;=\;}}$(som van drie derdemachten)

$\qquad~~~~$References Sum of Three Cubes

$\qquad~~~~$Getallen van de vorm $~9m+4~$ of $~9m+5~$ kunnen nooit als som van drie derdemachten geschreven worden.

$\qquad~~~~$In dit geval is $m\mathbf{\color{blue}{\;=\;}}11~~(+5)$.

$104\mathbf{\color{blue}{\;=\;}}$(som van vier derdemachten)

$\qquad~~~~(z\gt1000)$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+(-4)^3+(-7)^3+8^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{5^3+11^3+14^3+(-16)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{2^3+14^3+20^3+(-22)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+(-22)^3+(-28)^3+32^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{17^3+(-25)^3+(-28)^3+32^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-19)^3+(-37)^3+38^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{11^3+(-43)^3+(-46)^3+56^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-16)^3+32^3+68^3+(-70)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{5^3+(-28)^3+(-85)^3+86^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{41^3+(-46)^3+(-97)^3+98^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{5^3+(-49)^3+(-97)^3+101^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{77^3+(-88)^3+(-100)^3+107^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-31)^3+47^3+110^3+(-112)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{20^3+83^3+98^3+(-115)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-10)^3+(-79)^3+(-106)^3+119^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-70)^3+104^3+104^3+(-124)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{50^3+62^3+119^3+(-127)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+(-88)^3+(-112)^3+128^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{44^3+68^3+125^3+(-133)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{20^3+(-43)^3+(-154)^3+155^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{26^3+86^3+161^3+(-169)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+56^3+170^3+(-172)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{119^3+(-127)^3+(-172)^3+176^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{89^3+(-124)^3+(-169)^3+182^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-85)^3+104^3+182^3+(-187)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{98^3+134^3+152^3+(-190)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-130)^3+164^3+182^3+(-202)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+98^3+194^3+(-202)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-10)^3+(-154)^3+(-172)^3+206^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{140^3+146^3+158^3+(-214)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-76)^3+(-100)^3+(-214)^3+224^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{125^3+155^3+227^3+(-259)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+116^3+251^3+(-259)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{41^3+194^3+224^3+(-265)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{59^3+(-187)^3+(-232)^3+266^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-109)^3+(-124)^3+(-280)^3+293^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{38^3+(-205)^3+(-259)^3+296^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{77^3+203^3+287^3+(-319)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-64)^3+(-106)^3+(-346)^3+350^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{38^3+281^3+287^3+(-358)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{110^3+(-238)^3+(-328)^3+362^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{128^3+(-154)^3+(-358)^3+362^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+98^3+374^3+(-376)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-133)^3+149^3+398^3+(-400)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-52)^3+104^3+404^3+(-406)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{77^3+185^3+395^3+(-409)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+(-187)^3+(-406)^3+419^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{14^3+194^3+410^3+(-424)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{62^3+(-262)^3+(-400)^3+434^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{227^3+(-259)^3+(-430)^3+440^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{5^3+287^3+401^3+(-445)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{134^3+(-316)^3+(-406)^3+458^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-28)^3+(-85)^3+(-460)^3+461^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{197^3+203^3+440^3+(-466)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{92^3+164^3+461^3+(-469)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-64)^3+176^3+461^3+(-469)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{122^3+131^3+518^3+(-523)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-70)^3+356^3+488^3+(-544)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-16)^3+(-154)^3+(-550)^3+554^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-259)^3+(-352)^3+(-517)^3+584^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{332^3+(-436)^3+(-556)^3+602^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{527^3+(-550)^3+(-583)^3+602^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-358)^3+380^3+608^3+(-616)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{134^3+(-259)^3+(-613)^3+626^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-220)^3+236^3+644^3+(-646)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{71^3+182^3+650^3+(-655)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-67)^3+(-100)^3+(-658)^3+659^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{14^3+362^3+626^3+(-664)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{296^3+(-301)^3+(-667)^3+668^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{89^3+308^3+647^3+(-670)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-196)^3+470^3+593^3+(-673)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+224^3+680^3+(-688)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-256)^3+(-406)^3+(-628)^3+692^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{392^3+(-496)^3+(-646)^3+692^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-136)^3+362^3+668^3+(-700)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-112)^3+(-382)^3+(-670)^3+710^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{212^3+(-322)^3+(-697)^3+713^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-241)^3+560^3+593^3+(-718)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{326^3+467^3+644^3+(-739)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-46)^3+515^3+644^3+(-739)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{230^3+362^3+704^3+(-742)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-280)^3+506^3+692^3+(-760)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-304)^3+(-757)^3+773^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-154)^3+266^3+791^3+(-799)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+392^3+776^3+(-808)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-19)^3+(-589)^3+(-700)^3+818^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+(-403)^3+(-784)^3+818^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{116^3+248^3+833^3+(-841)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{173^3+419^3+812^3+(-850)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-508)^3+(-535)^3+(-697)^3+854^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-322)^3+(-625)^3+(-706)^3+857^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{212^3+524^3+794^3+(-868)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-436)^3+455^3+866^3+(-871)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-463)^3+(-643)^3+(-673)^3+875^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{14^3+(-544)^3+(-802)^3+878^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-502)^3+584^3+854^3+(-886)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-4)^3+(-574)^3+(-802)^3+890^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-445)^3+(-637)^3+(-715)^3+893^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{698^3+(-778)^3+(-838)^3+896^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{482^3+(-514)^3+(-886)^3+896^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-43)^3+410^3+875^3+(-904)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-136)^3+245^3+899^3+(-904)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-454)^3+(-658)^3+(-718)^3+908^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-154)^3+206^3+920^3+(-922)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{728^3+(-739)^3+(-916)^3+923^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-391)^3+734^3+791^3+(-940)^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{140^3+(-358)^3+(-940)^3+956^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-274)^3+(-742)^3+(-844)^3+1010^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{20^3+(-385)^3+(-991)^3+1010^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{236^3+(-784)^3+(-886)^3+1052^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-217)^3+(-727)^3+(-940)^3+1070^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-22)^3+(-850)^3+(-904)^3+1106^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\bbox[3px,border:1px green solid]{(-721)^3+(-814)^3+(-922)^3+1193^3}\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~(z\gt1000)$

$104\mathbf{\color{blue}{\;=\;}}$(som van vijf vijfdemachten)

$\qquad~~~~$(fully searched up to $z=1000)$

$\qquad~~~~\bbox[lightyellow,3px,border:1px blue solid]{~oplossing~onbekend~}\mathbf{\color{blue}{\;=\;}}$

$104\mathbf{\color{blue}{\;=\;}}$(som van zeven zevendemachten)

$\qquad~~~~\bbox[3px,border:1px blue solid]{6^7+10^7+(-11)^7+(-32)^7+(-39)^7+(-47)^7+49^7}$

104.2

$104^2\mathbf{\color{blue}{\;=\;}}[2^{15}][8^5][32^3]-28^3\mathbf{\color{blue}{\;=\;}}40^2+96^2\mathbf{\color{blue}{\;=\;}}112^2-12^3\mathbf{\color{blue}{\;=\;}}130^2-78^2\mathbf{\color{blue}{\;=\;}}185^2-153^2\mathbf{\color{blue}{\;=\;}}221^2-195^2\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\,\,346^2-330^2\mathbf{\color{blue}{\;=\;}}680^2-672^2\mathbf{\color{blue}{\;=\;}}1354^2-1350^2\mathbf{\color{blue}{\;=\;}}2705^2-2703^2\mathbf{\color{blue}{\;=\;}}5512^2-312^3$

$104^3\mathbf{\color{blue}{\;=\;}}13^5+91^3\mathbf{\color{blue}{\;=\;}}105^3-181^2\mathbf{\color{blue}{\;=\;}}208^2+1040^2\mathbf{\color{blue}{\;=\;}}260^3-4056^2\mathbf{\color{blue}{\;=\;}}312^3-5408^2\mathbf{\color{blue}{\;=\;}}592^2+880^2\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\,\,1092^2-260^2\mathbf{\color{blue}{\;=\;}}1170^2-494^2\mathbf{\color{blue}{\;=\;}}1183^2-65^3\mathbf{\color{blue}{\;=\;}}1344^2-88^3\mathbf{\color{blue}{\;=\;}}1560^2-1144^2\mathbf{\color{blue}{\;=\;}}1833^2-1495^2\mathbf{\color{blue}{\;=\;}}$

$\qquad~~~~\,\,2325^2-2069^2\mathbf{\color{blue}{\;=\;}}2808^2-2600^2\mathbf{\color{blue}{\;=\;}}4458^2-4330^2\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{5460^2-5356^2}\mathbf{\color{blue}{\;=\;}}8820^2-8756^2$

104.3

$104^2\mathbf{\color{blue}{\;=\;}}17^3+24^3-89^2\mathbf{\color{blue}{\;=\;}}78^3+98^3-112^3\mathbf{\color{blue}{\;=\;}}-780^3-1132^3+1244^3\mathbf{\color{blue}{\;=\;}}\cdots$

104.4

$104^3\mathbf{\color{blue}{\;=\;}}-13^3-51^3+108^3\mathbf{\color{blue}{\;=\;}}68^3-144^3+156^3\mathbf{\color{blue}{\;=\;}}-78^3-130^3+156^3\mathbf{\color{blue}{\;=\;}}\cdots~~$ (drie van vele oplossingen)

104.5

$104$ als resultaat met breuken waarin de cijfers van $0$ tot $9$ exact één keer voorkomen : ($3$ oplossingen) :
$614328/5907\mathbf{\color{blue}{\;=\;}}618072/5943\mathbf{\color{blue}{\;=\;}}823056/7914\mathbf{\color{blue}{\;=\;}}104$

104.6

Men moet $104$ tot minimaal de $38370$ste macht verheffen opdat in de decimale expansie exact $104$ $104$'s verschijnen.
Terloops : $104$$^{38370}$ heeft een lengte van $77394$ cijfers.

104.7

$104$ is op vijf verschillende wijzen de som van twee priemgetallen.

$$ 2~odd~primes \left[ \begin{matrix} &3&+&101\\ &7&+&97\\ &31&+&73\\ &37&+&67\\ &43&+&61 \end{matrix} \right. $$

104.8

Als som met de vier operatoren $+-*\;/$
$104\mathbf{\color{blue}{\;=\;}}(26+1)+(26-1)+(26*1)+(26/1)$

104.9

$3$$^{104}$$\mathbf{\color{blue}{\;=\;}}41745579179292917813953351511015323088870709282081$ is de hoogst gekende macht van $3$ waarbij

geen cijfer $6$ voorkomt in de decimale expansie. (OEIS A131616)

104.10

Voor $n\mathbf{\color{blue}{\;=\;}}104~~$ geldt $~~{\large\phi}(n)\mathbf{\color{blue}{\;=\;}}{\large\phi}(n+1) ~~\to~~ {\large\phi}(104)\mathbf{\color{blue}{\;=\;}}{\large\phi}(105)\mathbf{\color{blue}{\;=\;}}48~~~~({\large\phi}$ of 'phi' staat voor totiënt)

Zie ook bij en (OEIS A001274)

104.11

Voor $n\mathbf{\color{blue}{\;=\;}}104~~$ geldt $~~{\large\sigma}(n)\mathbf{\color{blue}{\;=\;}}{\large\sigma}(n+12) ~~\to~~ {\large\sigma}(104)\mathbf{\color{blue}{\;=\;}}{\large\sigma}(116)\mathbf{\color{blue}{\;=\;}}210~~~~({\large\sigma}$ of 'sigma' staat voor som der delers)

$104$ is de tweede oplossing uit (OEIS A015882)

104.12

$\begin{align}104\mathbf{\color{blue}{\;=\;}}\left({\frac{4}{3}}\right)^3+\left({\frac{14}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}\color{tomato}{\left({\frac{2*2}{3}}\right)^3+\left({\frac{7*2}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}\left({\frac{2}{3}}\right)^3+\left({\frac{7}{3}}\right)^3\mathbf{\color{blue}{\;=\;}}{\frac{104}{8}}\mathbf{\color{blue}{\;=\;}}13}\end{align}$

(Integral Sum of Two Rational Cubes) (OEIS A020898) (OEIS A228499) (Links uit OEIS A060838)

$(x^3+y^3)/z^3\mathbf{\color{blue}{\;=\;}}n~\to~$ [x waarde] (OEIS A190356) [y waarde] (OEIS A190580) [z waarde] (OEIS A190581)

Kleinste positieve oplossingen $~\to~$ [x waarde] (OEIS A254326) [y waarde] (OEIS A254324)

104.13

Som der reciproken van partitiegetallen van $104$ is $1$ op $157$ (honderdzevenenvijftig) wijzen.

Zes partities hebben unieke termen.

$~~(2)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}2+3+20+21+28+30}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{2}}+{\Large\frac{1}{3}}+{\Large\frac{1}{20}}+{\Large\frac{1}{21}}+{\Large\frac{1}{28}}+{\Large\frac{1}{30}}$

$~~(4)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}2+4+7+21+28+42}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{2}}+{\Large\frac{1}{4}}+{\Large\frac{1}{7}}+{\Large\frac{1}{21}}+{\Large\frac{1}{28}}+{\Large\frac{1}{42}}$

$(12)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}2+6+8+14+15+24+35}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{2}}+{\Large\frac{1}{6}}+{\Large\frac{1}{8}}+{\Large\frac{1}{14}}+{\Large\frac{1}{15}}+{\Large\frac{1}{24}}+{\Large\frac{1}{35}}$

$(21)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}3+4+6+9+16+18+48}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{3}}+{\Large\frac{1}{4}}+{\Large\frac{1}{6}}+{\Large\frac{1}{9}}+{\Large\frac{1}{16}}+{\Large\frac{1}{18}}+{\Large\frac{1}{48}}$

$(43)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}3+5+7+9+14+18+20+28}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{3}}+{\Large\frac{1}{5}}+{\Large\frac{1}{7}}+{\Large\frac{1}{9}}+{\Large\frac{1}{14}}+{\Large\frac{1}{18}}+{\Large\frac{1}{20}}+{\Large\frac{1}{28}}$

$(79)~~\bbox[navajowhite,3px,border:1px solid]{104\mathbf{\color{blue}{\;=\;}}4+5+6+7+10+14+28+30}~~$ en $~~1\mathbf{\color{blue}{\;=\;}}{\Large\frac{1}{4}}+{\Large\frac{1}{5}}+{\Large\frac{1}{6}}+{\Large\frac{1}{7}}+{\Large\frac{1}{10}}+{\Large\frac{1}{14}}+{\Large\frac{1}{28}}+{\Large\frac{1}{30}}$

(OEIS A125726)

104.14

○–○–○

$104^2\mathbf{\color{blue}{\;=\;}}10816~~$ en $~~108-\sqrt{16}\mathbf{\color{blue}{\;=\;}}108+prime(1)-6\mathbf{\color{blue}{\;=\;}}104$
$104^3\mathbf{\color{blue}{\;=\;}}1124864~~$ en $~~-1-1+24+86-4\mathbf{\color{blue}{\;=\;}}104$
$104^4\mathbf{\color{blue}{\;=\;}}116985856~~$ en $~~1+1+6+9*8+5+8+5+6\mathbf{\color{blue}{\;=\;}}104$
$104^5\mathbf{\color{blue}{\;=\;}}12166529024~~$ en $~~1-2-1+66+5+2+9+0+24\mathbf{\color{blue}{\;=\;}}104$
$104^6\mathbf{\color{blue}{\;=\;}}1265319018496~~$ en $~~126-5+3-1-9+0+1+8-4-9-6\mathbf{\color{blue}{\;=\;}}104$
$104^7\mathbf{\color{blue}{\;=\;}}131593177923584~~$ en $~~1+3+1+5-9+3+1+7+7-9+2+3+5+84\mathbf{\color{blue}{\;=\;}}104$
$104^8\mathbf{\color{blue}{\;=\;}}13685690504052736~~$ en $~~-1+3+6+8+5+6+9+0+5+0+40+5+2+7+3+6\mathbf{\color{blue}{\;=\;}}104$
$104^9\mathbf{\color{blue}{\;=\;}}1423311812421484544~~$ en $~~142+33-118+1+2+4+21+4+8+4-5+4+4\mathbf{\color{blue}{\;=\;}}104$

104.15

Som Der Cijfers ($sdc$) van $k^{\large{104}}$ is gelijk aan het grondtal $k$. De triviale oplossingen $0$ en $1$ negerend vinden we :

$\qquad\qquad~sdc\left(1377^{\large{104}}\right)\mathbf{\color{blue}{\;=\;}}1377\qquad\qquad~sdc\left(1476^{\large{104}}\right)\mathbf{\color{blue}{\;=\;}}1476$

104.16

Expressie met tweemaal de cijfers uit het getal $104$ enkel met operatoren $+,-,*,/,(),$^^
$104\mathbf{\color{blue}{\;=\;}}(1$^^$0$^^$4)+1*0*4$

104.17

Als expressie met enkelcijferige toepassing, resp. van $1$ tot $9~~$ (met dank aan Inder. J. Taneja).
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}(11-1)^{(1+1)}+1+1+1+1$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}2*2*(22+2+2)$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}3+3+3*33-3/3$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}4*4+44+44$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}(5^5-5)/(5*5+5)$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}(666-6)/6-6$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}777/7-7$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}88+8+8$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}(999+9+9)/9-9$

104.18

Met de cijfers van $1$ tot $9$ in stijgende en dalende volgorde (met dank aan Inder. J. Taneja) :
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}1+23+4+5+6+7*8+9$
$\qquad\qquad104\mathbf{\color{blue}{\;=\;}}9+8+7+65+4*3+2+1$

104.19

Het kleinste getal dat exact $104$ delers heeft is $430080\mathbf{\color{blue}{\;=\;}}2^{12}*3*5*7~~$ (OEIS A005179)

104.20

$104$ is het aantal partities van $23$ met verschillende termen. (OEIS A000009)
Onderstaande Pari/GP code zet ze allemaal op een rijtje.
q=partitions(23); c=0; for(i=1,#q, z=q[i]; f=1; for(j=1,#z-1, if(z[j]==z[j+1], f*=0));if(f, c++; print(c," ",q[i])))

104.21

(vijf multigrades) $104\to104^5\to$

\begin{aligned} 104^1&\mathbf{\color{blue}{\;=\;}}228^1+422^1-596^1-678^1+728^1\\ 104^5&\mathbf{\color{blue}{\;=\;}}228^5+422^5-596^5-678^5+728^5\\ \\ 104^1&\mathbf{\color{blue}{\;=\;}}273^1+559^1-806^1-884^1+962^1\\ 104^5&\mathbf{\color{blue}{\;=\;}}273^5+559^5-806^5-884^5+962^5\\ \\ 104^1&\mathbf{\color{blue}{\;=\;}}344^1+872^1-1272^1-1288^1+1448^1\\ 104^5&\mathbf{\color{blue}{\;=\;}}344^5+872^5-1272^5-1288^5+1448^5\\ \\ 104^1&\mathbf{\color{blue}{\;=\;}}-92^1-1108^1+1384^1+1668^1-1748^1\\ 104^5&\mathbf{\color{blue}{\;=\;}}-92^5-1108^5+1384^5+1668^5-1748^5\\ \\ 104^1&\mathbf{\color{blue}{\;=\;}}416^1+1304^1-1836^1-1872^1+2092^1\\ 104^5&\mathbf{\color{blue}{\;=\;}}416^5+1304^5-1836^5-1872^5+2092^5\\ \end{aligned}

104.22

$104$ is het aantal diagonalen in een zestienhoek $~~(n*(n-3)/2~$ met $~n\mathbf{\color{blue}{\;=\;}}16)$. (OEIS A000096)

104.23

$104$ vormt een Ruth-Aaron-paar samen met $105$. De sommen van hun priemfactoren zijn gelijk.
Zie het volledige verhaal bij en (OEIS A006145)

104.24

Kleinste oplossing voor de positieve Pell vergelijking $x^2-D*y^2\mathbf{\color{blue}{\;=\;}}1~$ met $D\mathbf{\color{blue}{\;=\;}}104$.

Als $D$ een kwadraat is dan zijn er geen oplossingen.

$\qquad{\color{darkviolet}{51}}^2-104*{\color{darkviolet}{5}}^2\mathbf{\color{blue}{\;=\;}}1$

(Pell equation solver)

104.25

De reciprook van $104$ heeft als decimale periode de waarde $DP(1/104)\mathbf{\color{blue}{\;=\;}}6$.
De lengte van het deel na de komma, voor het repeterende deel, wordt bepaald door de exponenten van
de priemfactoren $2$ en/of $5$. Het grootste aantal bepaalt het aantal tussenliggende cijfers. In dit geval zijn dat er $3$.
De volledige decimale expansie van $1$ periode na de $0,009$ is

$615{\color{darkcyan}{384}}$

(OEIS A001913) (OEIS A051626) (OEIS A060284)

("In case anyone was curious - inverse.txt" by Philip Clarke)

Splitst men deze periode van $6$ cijfers in twee gelijke groepen van $3$ cijfers dan is de som van elk tweetal cijfers
onder elkaar steeds $9$.

104.26

\(104\)	\(2^3*13\)	\(8\)	\(210\)
	\(1,2,4,8,13,26,52,104\)
	\(1101000_2\)	\(150_8\)	\(68_{16}\)

radix	omzetting	radix	omzetting
2		20
3		21
4		22
5		23
6		24
7		25
8		26
9		27
10		28
11		29
12		30
13		31
14		32
15		33
16		34
17		35
18		36
19		F5 = CLEAR