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MK-MO 2015 Problem 5

    Find all natural numbers mm having exactly three prime divisors p,q,rp,q,r , such that p−1∣m;qr−1∣m;q−1∤m;r−1∤m;3∤q+r.p-1\mid m; qr-1 \mid m; q-1 \nmid m; r-1 \nmid m; 3 \nmid q+r.

    Dataset text AI-MO AoPS. Quoted with source.

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