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TH-TMO 2011 Problem 1

    Given a natural number nn ≥3\geq 3 . If p,qp,q are primes, such that, p∣n!p \mid n! and q∣(n−1)!−1q \mid (n-1)!-1 . Prove that, p<qp<q

    Dataset text AI-MO AoPS. Quoted with source.

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