  The paper assesses the top number of integer solutions for algebraic
Diophantine Thue diagonal equation of the degree $n \geq 2$ and number of
variables $k > 2$ and equations with explicit variable in the case when the
coefficients of the equation are of the opposite signs. The author found
integer conversions that maintain the asymptotic behavior of the number of
integer solutions of algebraic Diophantine equation in the case of the
conversion equation to diagonal form. The paper considers the estimation of the
number of integer solutions for some types of algebraic Diophantine equations
with nondiagonal form.
