IMO Shortlist 2015 problem N3


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30. kolovoza 2018.
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Let m and n be positive integers such that m>n. Define x_k=\frac{m+k}{n+k} for k=1,2,\ldots,n+1. Prove that if all the numbers x_1,x_2,\ldots,x_{n+1} are integers, then x_1x_2\ldots x_{n+1}-1 is divisible by an odd prime.

(Austria)

Izvor: https://www.imo-official.org/problems/IMO2015SL.pdf