Home Competitions IR-TST 2020 Problem 12
p p p p − 1 2 \frac{p-1}2 2 p − 1 ( x 1 , x 2 , … , x p − 1 2 ) ∈ Z p p − 1 2 \left(x_1,x_2,\dots,x_{\frac{p-1}2}\right)\in \mathbb{Z}_p^{\frac{p-1}2} ( x 1 , x 2 , … , x 2 p − 1 ) ∈ Z p 2 p − 1 ∑ i = 1 p − 1 2 x i ≡ ∑ i = 1 p − 1 2 x i 2 ≡ ⋯ ≡ ∑ i = 1 p − 1 2 x i p − 1 2 ( m o d p ) . \sum_{i = 1}^{\frac{p-1}{2}} x_{i} \equiv \sum_{i = 1}^{\frac{p-1}{2}} x_{i}^{2} \equiv \cdots \equiv \sum_{i = 1}^{\frac{p-1}{2}} x_{i}^{\frac{p - 1}{2}} \pmod p. i = 1 ∑ 2 p − 1 x i ≡ i = 1 ∑ 2 p − 1 x i 2 ≡ ⋯ ≡ i = 1 ∑ 2 p − 1 x i 2 p − 1 ( mod p ) . Proposed by Ali Partofard
Dataset text AI-MO AoPS . Quoted with source.
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