Transcendental solutions of diophantine equations
โ Scribed by M. G. Zaidenberg
- Publisher
- Springer US
- Year
- 1989
- Tongue
- English
- Weight
- 291 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0016-2663
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this study, we investigate positive integer solutions of the Diophantine equations x 2 -kxyโy 2 โx = 0 and x 2 -kxy-y 2 โy = 0. It is shown that when k > 3, x 2 -kxy+y 2 +x = 0 has no positive integer solutions but the equation x 2 -kxy + y 2 -x = 0 has positive integer solutions. Moreover, it is
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
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.