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Omni-MATH / Let p≥3 be a prime number and 0≤r≤p−3. Let x₁,x₂,…,x_(p−1+r) be integers satisfying sum_{i=1}^{p-1+r}x_i^kequiv r bmod{p}for all 1≤k≤p−2. What are the possible remainders of number…

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problem

Let p≥3p\geq 3 be a prime number and 0≤r≤p−3.0\leq r\leq p-3. Let x1,x2,…,xp−1+rx_1,x_2,\ldots,x_{p-1+r} be integers satisfying \[\sum_{i=1}^{p-1+r}x_i^k\equiv r \bmod{p}\]for all 1≤k≤p−2.1\leq k\leq p-2. What are the possible remainders of numbers x2,x2,…,xp−1+rx_2,x_2,\ldots,x_{p-1+r} modulo $p?$
Plain-text mathematical notation (without MathML)
Let p≥3 be a prime number and 0≤r≤p−3. Let x₁,x₂,…,x_(p−1+r) be integers satisfying \[\sum_{i=1}^{p-1+r}x_i^k\equiv r \bmod{p}\]for all 1≤k≤p−2. What are the possible remainders of numbers x₂,x₂,…,x_(p−1+r) modulo $p?$
Original LaTeX notation
Let $p\geq 3$ be a prime number and $0\leq r\leq p-3.$ Let $x_1,x_2,\ldots,x_{p-1+r}$ be integers satisfying \[\sum_{i=1}^{p-1+r}x_i^k\equiv r \bmod{p}\]for all $1\leq k\leq p-2.$ What are the possible remainders of numbers $x_2,x_2,\ldots,x_{p-1+r}$ modulo $p?$

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Source and history

task_id
6c77743f-8511-5b16-ba56-5c5e3677e455
task_key
test--6c77743f-8511-5b16-ba56-5c5e3677e455
task_revision_id
1
config / split
/ test

Official source

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