Question

prove that if x and y are both odd positive integer, then x^2+y^2 is even but not divisible by 4.
$a = bq + r 0 < r < b$
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Answer 1

Step-by-step explanation:

Let the two positive number be x=2m+1 and y=2n+1

x²+y² = (2m+1)² + (2n+1)²

= 4m²+4m+1+ 4n²+4n+1

= 4 ( m²+m +n²+n) + 2

So, we can observe that the sum of squares is even the number not divisible by 4.

Hence proved