Q. 535.0( 1 Vote )

If m & n are

Answer :

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

Now,


m2 + n2 = (2x+1)2 + (2y+1)2


m2 + n2 = 4 x2 + 4x + 1 + 4 y2 + 4y + 1


m2 + n2 = 4 (x2 + y2 + x + y ) + 2


So, on dividing m2 + n2 by 4, 2 will be the remainder and a quotient would be (x2 + y2 + x + y ).


So m2 + n2 is even but not divisible by 4


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