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10. Let P(k) be the following statement: ”Let a1, a2, . . . , ak be...

10. Let P(k) be the following statement: ”Let a1, a2, . . . , ak be integers and p be a prime. If p|(a1 · a2 · a3 · · · ak), then p|ai for some i with 1 ≤ i ≤ k.” Prove that P(k) holds for all positive integers k

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