# A Fermat's Problem

**Number Theory**Level 4

How many pairs \((x, y)\) of non-negative integers with \(0\le x\le y\) satisfy the equation \(5{ x }^{ 2 }-4xy+2x+{ y }^{ 2 }=624\)?

How many pairs \((x, y)\) of non-negative integers with \(0\le x\le y\) satisfy the equation \(5{ x }^{ 2 }-4xy+2x+{ y }^{ 2 }=624\)?

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