Determine all ordered pairs that satisfy $(x-y)^{2}+x^{2}=25$, where $x$ and $y$ are integers and $x \geq 0$. The number of different values of $y$ that occur is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Solution

Since 25 is the sum of two squares, the only possible values for $x$ are $0,3,4$ and 5 . Substituting each value of $x$ into the equation and finding the corresponding value of $y$ gives five different values for $y$.

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