Two distinct case, Engineering Mathematics

A) Prove the following theorem by considering two distinct cases. For any integer n, n2 + n is even.

B)  If x = r - s2 and y = 2rs for any integers r and s, then x2 + y2 = z2 for some nonnegative integer z. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement

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A) Prove the following theorem by considering two distinct cases. For any integer n, n 2 + n is even. B)  If x = r 2  - s 2 and y = 2rs for any integers r and s, then x 2 +


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