Chevalley–Warning theorem

In number theory, the Chevalley–Warning theorem implies that certain polynomial equations in sufficiently many variables over a finite field have solutions. It was proved by Ewald Warning (1935) and a slightly weaker form of the theorem, known as Chevalley's theorem, was proved by Chevalley (1935). Chevalley's theorem implied Artin's and Dickson's conjecture that finite fields are quasi-algebraically closed fields (Artin 1982, page x).