A Computer-Based Approach to Solving the Diophantine Equation $7^x-3^y=100$

  • Andreea Dima University of Bucharest
Keywords: exponential diophantine equation; prime number; order of an integer modulo another integer

Abstract

Assisted by Octave and by a website where one can find the order of a modulo m (here a and m are relatively prime natural numbers), I found a proof for showing that the diophantine equation $7^x - 3^y = 100$ has only the solution (x,y) = (3,5) in positive integers.

Published
2022-07-22
How to Cite
Dima, A. (2022). A Computer-Based Approach to Solving the Diophantine Equation $7^x-3^y=100$. The PUMP Journal of Undergraduate Research, 5, 161-164. Retrieved from https://journals.calstate.edu/pump/article/view/2874