The paper assesses the top number of integer solutions of algebraic Diophantine Thue diagonal equation with 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 have opposite signs. The author found integer conversions that preserve 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 of some types of algebraic not diagonal Diophantine equations.
Estimations of the number of solutions of algebraic Diophantine equations with natural coefficients using the circle method of Hardy-Littlewood
On integer solutions to x^5 - (x+1)^5 -(x+2)^5 +(x+3)^5 = 5^m + 5^n
Converting of algebraic Diophantine equations to a diagonal form with the help of generalized integer orthogonal transformation, maintaining the asymptotic behavior of the number of its integer solutions
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