The Waring-Goldbach problem (Q2862856)

Let \(n\) be a positive integer. The main contribution of the paper under review is the following theorem. There exist constants \(V=V(n)\) and \(c=c(n)\) (depending on \(n\) only) such that every positive integer \(N\geq c\) can be written as a sum \(N=p_1^n+\ldots+p_r^n\) where \(p_1\), \dots, \(p_r\) are primes, and \(r\leq V\). The proof uses some ideas of the proof given by Vinogradov in the 1930s for the estimates of the Waring problem.