Positive integers a and b are such that (15a+16b) and (16a-15b) are perfect squares. Find the least possible value of the smaller of these two squares.

(In reply to Solution by xdog)

If non-zero squares aren't disallowed, then that is a perfectly good solution.

However, here is the definition given on www.mathworld.wolfram.com which lists "1" as the first square number:

A square number is a figurate number of the form <IMG class=inlineformula height=16 alt=S_n==n^2 src="http://mathworld.wolfram.com/images/equations/SquareNumber/inline1.gif" width=45 border=0>, where <IMG class=inlineformula height=15 alt=n src="http://mathworld.wolfram.com/images/equations/SquareNumber/inline2.gif" width=7 border=0> is an integer. A square number is also called a perfect square. The first few square numbers are 1, 4, 9, 16, 25, 36, 49, ... (Sloane's A000290).

Sloane's A00290, interestingly enough, includes "0" as the start of the sequence.

Posted by Mindy Rodriguez on 2005-11-09 21:26:17