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

Integer conversions and estimation of the number of integer solutions of algebraic Diophantine equations