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2014-09-16T16:28:24+05:30

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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


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