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Complete residue systems

Source: Pre-VMO 2012 - Problem 5

November 27, 2011
abstract algebranumber theory proposednumber theory

Problem Statement

Determine all values of nn satisfied the following condition: there's exist a cyclic (a1,a2,a3,...,an)(a_1,a_2,a_3,...,a_n) of (1,2,3,...,n)(1,2,3,...,n) such that {a1,a1a2,a1a2a3,...,a1a2...an}\left\{ {{a_1},{a_1}{a_2},{a_1}{a_2}{a_3},...,{a_1}{a_2}...{a_n}} \right\} is a complete residue systems modulo nn.
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