This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 1

1998 Turkey Team Selection Test, 3
Tags: polynomial , algebra , combinatorial nullstellensatz , number theory
Let $f(x_{1}, x_{2}, . . . , x_{n})$ be a polynomial with integer coefficients of degree less than $n$. Prove that if $N$ is the number of $n$-tuples $(x_{1}, . . . , x_{n})$ with $0 \leq x_{i} < 13$ and $f(x_{1}, . . . , x_{n}) = 0 (mod 13)$, then $N$ is divisible by 13.