Data Sufficiency (DS) | Re: If p, x, and y are positive integers, y is odd, and p = x^2

If p, x, and y are positive integers, y is odd, and p = x^2 + y^2, is x divisible by 4?

(1) When p is divided by 8, the remainder is 5 -->\(p=8q+5=x^2+y^2\) --> as given that\(y=odd=2k+1\) -->\(8q+5=x^2+(2k+1)^2\) -->\(x^2=8q+4-4k^2-4k=4(2q+1-k^2-k)\) .

So,\(x^2=4(2q+1-k^2-k)\) . Now, if\(k=odd\) then\( 2q+1-k^2-k=even+odd-odd-odd=odd\)
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