[ *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.

__8778__^{2} + 10296^{2} = 13530^{2}

or

(T_{132})^{2} + (T_{143})^{2} = (T_{164})^{2}

It so happens that the smallest side T_{132} or 8778

( just like 132^{2} + 143^{2} = 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

1^{2} = 1 and 3^{2} = 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.