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Japan olympiad

Source: Japanese MO Finals 2000

January 20, 2005
algebra unsolvedalgebranumber theoryCombinatorial Number Theory

Problem Statement

Given a natural number n≥3n\ge 3, prove that there exists a set AnA_n with the following two properties: 1) AnA_n consists of nn distinct natural numbers 2) For any a∈Aa\in A, the remainder of the product of all elements of An\{a}A_n\backslash \{a\} divided by aa is 11.
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