(9) Let n and k be positive integers. Recall from lecture that a weak composition of n into k parts is a k-tuple (a₁,..., ak) of nonnegative integers such that a₁ + . . . + ak = n, while a (strong) composition of n into k parts is the same except a₁,..., a have to be positive integers. Find a bijection between the set of weak compositions of n into k parts and the set of strong compositions of n + k into k parts.

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A: Prove that for any integer a, 9 ⫮ (a2 – 3).

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