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Two sets- Iran 3rd round-Number Theory 2007

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July 28, 2010
modular arithmeticinequalitiesnumber theory unsolvednumber theory

Problem Statement

Let pp be a prime such that p≡3(mod4)p \equiv 3 \pmod 4. Prove that we can't partition the numbers a,a+1,a+2,⋯ ,a+p−2a,a+1,a+2,\cdots,a+p-2,(a∈Za \in \mathbb Z) in two sets such that product of members of the sets be equal.
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