Divisibility properties of various products of integers

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Prove that if x + y is even, then the product xy(x + y)(x - y) is divisible by 24, and that without this restriction, 4xy(x- y)(x + y) is divisible by 24. Consider that any integer is of the form 3k, 3k + 1, or 3k + 2 in showing that 3|xy(x + y)(x - y). Similarly, because any integer is of the form 8k, 8k + 1, ..., or 8k + 7, then 8|xy(x - y)(x + y).

Reference no: EM13121885

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