Determination of the asymptotic behavior of the number of natural solutions for certain types of diagonal Diophantine equations

Abstract

We obtain asymptotic upper bounds for the number of natural solutions of the following diagonal Diophantine equations in a hypercube with side - $N$ in the paper: $x_1=x_2^k+...+x_s^k$, $x_1^k=x_2^k+...+x_s^k$, $x_1={\sum }_{j=2}^s{x_j}^{k_j}$, where $k,s,k_j$ are the natural numbers.

20 pages

References in corpus (1)

• Converting of algebraic Diophantine equations to a diagonal form with the help of an integer non-orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutions