The Waring-Goldbach problem: one square and five cubes
Suppose that \(p_1, p_2, p_3, p_4, p_5\) are prime numbers and a natural number \(x\) has at most 36 prime factors, counted according to multiplicity. Let \(R(N)\) denote the number of solutions of the following equation \[ N=x^2+p_1^3+p_2^3+p_3^3+p_4^3+p_5^3. \] The author proves that \[ R(N)\geq c\, N^{\frac{19}{18}}/(\log N)^6, \] for an even and sufficiently large integer \(N\) with some absolute constant \(c\).
scientific article; zbMATH DE number 6348373
scientific article