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Tuymaada 2010, Junior League, Problem 6

Source:

July 18, 2010
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

We have a number nn for which we can find 5 consecutive numbers, none of which is divisible by nn, but their product is. Show that we can find 4 consecutive numbers, none of which is divisible by nn, but their product is.