Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?

Authors

  • D. Biswas Department of Physics, Santipur College, West Bengal-741404, India

DOI:

https://doi.org/10.3329/jsr.v14i3.58535

Abstract

This paper investigates the solutions (if any) of the Diophantine equation 3x + 35y = Z2, where  , x, y, and z are whole numbers. Diophantine equations are drawing the attention of researchers in diversified fields over the years. These are equations that have more unknowns than a number of equations. Diophantine equations are found in cryptography, chemistry, trigonometry, astronomy, and abstract algebra. The absence of any generalized method by which each Diophantine equation can be solved is a challenge for researchers. In the present communication, it is found with the help of congruence theory and Catalan’s conjecture that the Diophantine equation 3x + 35y = Z2 has only two solutions of  (x, y, z) as  (1, 0, 2) and (0, 1, 6) in non-negative integers.

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Published

2022-09-01

How to Cite

Biswas, D. (2022). Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?. Journal of Scientific Research, 14(3), 861–865. https://doi.org/10.3329/jsr.v14i3.58535

Issue

Section

Section A: Physical and Mathematical Sciences