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Problem 5 of First round

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

January 13, 2020
number theoryprime divisorsprime numbersDivisibility

Problem Statement

Does there exist a natural number nn with exactly 3 different prime divisors pp, qq, and rr, so that p−1∣np-1\mid n, qr−1∣nqr-1\mid n, q−1∤nq-1\nmid n, r−1∤nr-1\nmid n, and 3∤q+r3\nmid q+r?
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