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Let m = 2 x + 1 and n = 2 y + 1 where x and y are non-negative integers.

m² + n² = (2x+1)² + (2y+1)²

= 4 x² + 4x + 1 + 4 y² + 4y + 1

= 4 (x² + y² + x + y ) + 2

So when m² + n² is divided by 4, then we get a reminder of 2 and

a quotient of (x² + y² + x + y ).

So m² + n² is divisible by 4

m² + n² = (2x+1)² + (2y+1)²

= 4 x² + 4x + 1 + 4 y² + 4y + 1

= 4 (x² + y² + x + y ) + 2

So when m² + n² is divided by 4, then we get a reminder of 2 and

a quotient of (x² + y² + x + y ).

So m² + n² is divisible by 4