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Source: 11th XMO #3

February 13, 2023
prime numbersnumber theory

Problem Statement

Let pp is a prime and p≡2(mod3)p\equiv 2\pmod 3. For ∀a∈Z\forall a\in\mathbb Z, if p∣∏i=1p(i3−ai−1),p\mid \prod\limits_{i=1}^p(i^3-ai-1),then aa is called a "GuGu" number. How many "GuGu" numbers are there in the set {1,2,⋯ ,p}?\{1,2,\cdots ,p\}?
(We are allowed to discuss now. It is after 00:00 Feb 14 Beijing Time)
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