Question

If x and y are both odd positive integers then x square + y square is even but not divisible by 4

Answer 1

Answer:

Step-by-step explanation:

Let the two odd positive numbers be

X=2k+1 and Y=2p+1

Hence X^2+Y^2=(2k+1)^2+(2p+1)^2

=4k^2+4k+1+4p^2+4p+1

=4k^2+4p^2+4k+4p+2

=4(k^2±p^2+k+p)+2

Therefore, clearly notice that the sum of square is even the number is not divisible by 4

Hence if X and Y are odd positive integers, X^2+Y^2 is even but not divisible by 4.

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