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[ May 3, 2002 ] palindromes & reversible numbers in a most interesting manner : (1)n(4)n(4)n * (4)n(4)n(1)n = [ (2)n(5)n(2)n ]2 And the puzzle is... 144(0)n144 * 441(0)n441 = [ 252(0)n252 ]2 158(558)n4 * 4(855)n851 = [ 277(477)n2 ]2 "et la suivante, très jolie et très simple" (1584)n * (4851)n = [ (2772)n ]2 First he sampled the next three methods 144 * 441 = 2522 1584 * 4851 = 27722 12544 * 44521 = 236322 From that data he generalized these results If Q * R = P2 (R is the reverse of Q) Let Q = abc...xyz ; R = zyx...cba ; P = klm...mlk [(a)n(b)n(c)n...(x)n(y)n(z)n] * [(z)n(y)n(x)n...(c)n(b)n(a)n] = [a(0)nb(0)nc...x(0)ny(0)nz] * [z(0)ny(0)nx...c(0)nb(0)na] = Here are the first ten basic Q numbers which can be applied 144 Numbers like 10404, 114444 or 144144 are not included method + method = method + method The law of method composition is not commutative ! Let starting Q number be 1584 | |||
A000131 Prime Curios! Prime Puzzle Wikipedia 131 Le nombre 131 |
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