MathDB

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?

Proposed by Dávid Matolcsi, Budapest

A. 792