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[ October 6, 2002 ]
8778 a curious Palindromic Triangular.

Jean Claude Rosa (email) brought to my attention that there
is only one solution known for constructing a rectangular triangle
whose three sides are all triangular numbers.
Source : Puzzle 187. Triangles and Triangular numbers
situated at Carlos Rivera's PP&P website.
87782 + 102962 = 135302
or
(T132)2 + (T143)2 = (T164)2
It so happens that the smallest side T132 or 8778
( just like 1322 + 1432 = 37873 btw ) is palindromic !

JCR became obsessed with looking for another solution
but that must be like finding a needle in a haystack.
So to relax for a while (??!!) he searched for
Squares of triangular numbers that are palindromic
and besides these two trivial solutions
12 = 1 and 32 = 9
he didn't find a larger example.
Is this another needle in a still bigger haystack ?

ps. JCR thinks that he/she who discovers the next
trio of triangulars won't have found a needle
but rather a very beautiful jewel in the World!Of Numbers.


A000140 Prime Curios! Prime Puzzle
Wikipedia 140 Le nombre 140














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