Problem
NT-B1-M05-P014 A Larger Difference of Squares
#14
★★★☆☆ Level 3 of 5
Find all positive integer solutions of \(x^2-y^2=68\).
The factors \(x-y\) and \(x+y\) must have the same parity.
\((x-y)(x+y)=68\). The only suitable positive factor pair with the same parity is \((2,34)\). The pair \((4,17)\) has different parity. Thus \(x=\frac{2+34}{2}=18\), \(y=\frac{34-2}{2}=16\). The answer is \((18,16)\).
The problem trains filtering factor pairs by parity.