Question

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Answer 1

Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1

Hence x2 + y2 = (2k + 1)2 + (2p + 1)2

= 4k2 + 4k + 1 + 4p2 + 4p + 1

= 4k2 + 4p2 + 4k + 4p + 2

= 4(k2 + p2 + k + p) + 2

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, then x2 + y2 is even but not divisible by 4

Answer 2

x^2 - y^2 = (x+y) (x-y)
Since x & y are odd, so x+y & x-y are even.
The min. value of x-y is 2 here & x+y will be obviously greater than or equal to 4. So, (x+y) (x-y) will always be a multiple of 4.