Question

prove that if x nd y r odd +tive intgr then x²+y² is even but not divisible by 4

Answer 1

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

Step-by-step explanation:

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