Combinatorial Nullstellensatz

Explanations 4

• The theorem of Combinatorial Nullstellensatz is an extremely powerful statement regarding the points where a multivariate polynomial is allowed to vanish. This is useful in comb…

  By Lawrence Sun, Eric Zhang

• (EGZ Theorem) Let nnn be a positive integer. Prove that among 2n−12n-12n−1 integers, we can find nnn of them whose sum is divisible by nnn.

  By Lawrence Sun

• Let ppp be a prime. Consider a p×pp \times pp×p grid of points labelled (x,y)(x,y)(x,y) for 0≤x,y≤p−10 \le x,y \le p-10≤x,y≤p−1. Consider the p2+pp^2 + pp2+p ``lines'' which are…

  By Lawrence Sun

• (2007 IMO Problem 6) Let nnn be a positive integer. Consider S={(x,y,z)∣x,y,z∈{0,1,…,n},x+y+z>0}S = \left\{ (x,y,z) \mid x,y,z \in \{ 0, 1, \ldots, n\}, x + y +z > 0 \right \}S=…

  By Lawrence Sun