The solutions of the Diophantine equations 17^x-3^y=z^2  and 17^x-5^y=z^2

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Published: Jun 30, 2026
Keywords:
Diophantine equation Non-negative integer solution Congruence

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Poonchayar Patthanangkoor
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Phetrada Kunamee
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Sirinda Boonrueang
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120
Aphisit Phothisarit
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120

Abstract

In this paper, we investigated the non-negative integer solutions to the Diophantine equations  and .  The results showed that  and  are the only non-negative integer solutions for both equations.

Article Details

Issue
Vol.34 No.3 (May-June 2026)
Section
Physical Sciences

References

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