IMO 1971 LL SWE45

Let m and n denote integers greater than 1, and let u(n) be

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IMO 1971 LL SWE45

Origin: SWE

Problem

Let m and n denote integers greater than 1, and let \nu(n) be the number of primes less than or equal to n. Show that if the equation n \nu(n) = m has a solution, then so does the equation n \nu(n) = m −1.