[ October 6, 2002 ]
8778 a curious Palindromic Triangular
Jean Claude Rosa

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 .