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exist a1,a2,...,an for n-1-Iran 3rd round-Number Theory 2007

Source:

July 28, 2010

modular arithmeticnumber theory

Problem Statement

Prove that for any positive integer

n \geq 3

there exist positive integers

a_1,a_2,\cdots , a_n

such that

a_1a_2\cdots a_n \equiv a_i \pmod {a_i^2} \qquad \forall i \in \{1,2,\cdots ,n\}