๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The complete solution of a diophantine equation involving biquadrates

โœ Scribed by Ajai Choudhry

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
185 KB
Volume
110
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis

While parametric solutions of the diophantine equation s i=1 x 4 i = s i=1 y 4 i are known for any integral value of s 2, the complete solution in integers is not known for any value of s. In this paper, we obtain the complete solution of this equation when s 13.

๐Ÿ“œ SIMILAR VOLUMES

Polynomial Bounds for the Solutions of a
Polynomial Bounds for the Solutions of a Class of Diophantine Equations
โœ Dimitrios Poulakis ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 320 KB

Let K be an algebraic number field such that all the embeddings of K into C are real. We denote by O K the ring of algebraic integers of K. Let F(X, Y) be an irreducible polynomial in K[X, Y ]&K[Y ] of total degree N and of degree n>0 in Y. We denote by F N (X, Y ) its leading homogeneous part. Supp

On the Practical Solution of Genus Zero
On the Practical Solution of Genus Zero Diophantine Equations
โœ Dimitrios Poulakis; Evaggelos Voskos ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 263 KB

Let f (X, Y ) be an absolutely irreducible polynomial with integer coefficients such that the curve defined by the equation f (X, Y ) = 0 is of genus 0 having at least three infinite valuations. This paper describes a practical general method for the explicit determination of all integer solutions o

On the number of solutions of a diophant
On the number of solutions of a diophantine equation with symmetric entries
โœ M.Z. Garaev ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 117 KB

For a class of strictly increasing real valued functions f (n) we obtain an upper bound for the number of solutions of the equation f (y i ), 1 x 1 , . . . , y d N.