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product of some of members-Iran 3rd round-Number Theory 2007

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July 28, 2010
number theory unsolvednumber theory

Problem Statement

Let p≥3p \geq 3 be a prime and a1,a2,⋯ ,ap−2a_1,a_2,\cdots , a_{p-2} be a sequence of positive integers such that for every k∈{1,2,⋯ ,p−2}k \in \{1,2,\cdots,p-2\} neither aka_k nor akk−1a_k^k-1 is divisible by pp. Prove that product of some of members of this sequence is equivalent to 22 modulo pp.
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