If p and q are positive integers that satisfy 3p²+p=4q²+q, prove that p-q, 3p+3q+1 and 4p+4q+1 are squares of integers.

Start by proving that:

(p-q)(3p+3q+1)= q^2 (why?); and:

(p-q)(4p+4q+1) = p^2 (why?)

Edited on April 9, 2007, 12:13 pm

Posted by K Sengupta on 2007-04-09 05:55:15