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

2016/11/17 by Victor Volfson, Volfson, Victor
Mathematics · #11D45 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11D45

paper · pdf · doi:10.48550/arxiv.1611.05704

17 pages

arxiv created 2017/01/31 · arxiv updated 2017/02/01

Abstract

The paper assesses the top number of integer solutions for algebraic Diophantine Thue diagonal equation of the degree n ≥ 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.

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