MathDB

3

Part of the 11th XMO

Problems(1)

Another standard NT Cookie

Source: 11th XMO #3

2/13/2023
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)
prime numbersnumber theory