  This article discusses the question - how to estimate the number of solutions
of algebraic Diophantine equations with natural coefficients using Circular
method developed by Hardy and Littlewood. This paper considers the estimate of
the number of solutions of algebraic Diophantine equation:
$c_1x_1^{k_1}+c_2x_2^{k_2}+...+c_sx_s^{k_s}=n$. The author found the asymptotic
estimate for the number of solutions of this equation as a function of the
value $n$, if all coefficients and $n$ are natural. This article analyzes the
results and shows that these estimates of the number of natural solutions of
the equations have high accuracy.
