some short and selected math problems of different levels in random order I try to keep the ans simple
Saturday, October 6, 2012
Suppose two integers, m and n differ by 1. Suppose also that x, y, and a are integers such that x + a = m^2 and y + a = n^2. Show that xy + a is a perfect square.
without loss of generality as it is symmetric let m = n+ 1
x=(n+1)^2-a ;
y=n^2 -a
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