Applied Physics and Mathematics Annotation << Back INTEGER CONVERSIONS AND ESTIMATION OF THE NUMBER OF INTEGER SOLUTIONS OF ALGEBRAIC NOT DIAGONAL DIOPHANTINE EQUATIONS V.L. VOLFSON The paper assesses the top number of integer solutions of algebraic Diophantine Thue diagonal equation with the degree n ≥ 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. Keywords: algebraic Diophantine equation, Thue equation, equation with explicit variable, integer coeffi cients, constant term, diagonal, number of integer solutions, asymptotic estimate, upper bound, lower bound, hypercube, hypersphere, hypersurface hyperplane, integer conversions, motion conversion, rotation transformation, migration, deformation transformation, homothetic, canonical form, rotation matrix. Contacts: E-mail: znakvicvolf@mail.ru Pp. 51-58.