WON TOPIC 140

World!Of Numbers		WON plate 140 \|
[ 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 .
A000140 Prime Curios! Prime Puzzle Wikipedia 140 Le nombre 140