Problem
NT-B2-M07-P003 Difference of Squares
#3
★★☆☆☆ Level 2 of 5
Find all positive integers \(x>y\) such that \(x^2-y^2=105\).
Factor \(105\) as \((x-y)(x+y)\).
We write \((x-y)(x+y)=105\). The two factors must have the same parity; since the product is odd, both are odd. The factor pairs are \((1,105),(3,35),(5,21),(7,15)\). They give \((x,y)=(53,52),(19,16),(13,8),(11,4)\).
A good check of the parity restriction in a difference of squares.