Problem
ALG-B1-M01-P020 Integer Solutions by Factoring
#20
★★★★☆ Level 4 of 5
Find all integers \(x,y\) such that \(x^2-y^2=15\).
Factor the left side and list factor pairs of \(15\).
We have \((x-y)(x+y)=15\). The two factors have the same parity because their sum is \(2x\), even. Since \(15\) is odd, both are odd.
The possible pairs are \((1,15)\), \((3,5)\), \((-1,-15)\), \((-3,-5)\). Solving \(x-y=u\), \(x+y=v\), we get \((x,y)=(8,7),(4,1),(-8,-7),(-4,-1)\).
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