Problem
ALG-B1-M03-P009 Integer Solutions from Difference of Squares
#9
★★☆☆☆ Level 2 of 5
Find all integers \(x,y\) such that \(x^2-y^2=21\).
Factor the left side and list factor pairs of \(21\).
\((x-y)(x+y)=21\). The two factors have the same parity, and the product is odd, so both are odd.
The pairs \((1,21)\), \((3,7)\), \((-1,-21)\), \((-3,-7)\) give \((11,10)\), \((5,2)\), \((-11,-10)\), \((-5,-2)\).
Track the signs of factor pairs.