Problem
NT-B1-M05-P010 Difference of Squares \(56\)
#10
★★☆☆☆ Level 2 of 5
Find all positive integer solutions of \(x^2-y^2=56\).
Split \(56\) into two factors of the same parity.
\((x-y)(x+y)=56\). The two factors must have the same parity, so both are even. The suitable pairs are \((2,28)\) and \((4,14)\). They give \((x,y)=(15,13)\) and \((9,5)\).
The pair \((7,8)\) fails because the parities differ.