Problem
NT-B1-M05-P004 Difference of Squares
#4
★☆☆☆☆ Level 1 of 5
Find all positive integer solutions of \(x^2-y^2=15\).
Factor the left-hand side as \((x-y)(x+y)\).
We have \((x-y)(x+y)=15\). The positive factor pairs with the same parity are \((1,15)\) and \((3,5)\). They give \((x,y)=(8,7)\) and \((4,1)\). These are all solutions.
Make sure \(x+y\) is greater than \(x-y\).