Solution of the Exponential Diophantine Equation 10ð’™ âˆ’ðŸðŸ—ð’š = ð’›ðŸ

Deepak Gupta

Solution of the Exponential Diophantine Equation 10ð’™ âˆ’ðŸðŸ—ð’š = ð’›ðŸ

Deepak Gupta Assistant Professor, Department of Mathematics, M M (P G) College, Modinagar, Ghaziabad, Uttar Pradesh, India

Abstract

The Diophantine equation 10^ð‘¥ âˆ’ 29^ð‘¦ = ð‘§², where ð‘¥,ð‘¦,ð‘§ are non negative integers, has been examined by the author of this paper. By applying modular arithmetic method and Catalanâ€™s Conjecture, we showed that (ð‘¥,ð‘¦,ð‘§) = (0,0,0) and (1,0,3) are two non-negative integer solutions of this Diophantine equation.

Published

2025-07-22

How to Cite

GUPTA, Deepak. Solution of the Exponential Diophantine Equation 10ð’™ âˆ’ðŸðŸ—ð’š = ð’›ðŸ. Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 10, p. 8-11, july 2025. ISSN 2455-7021. Available at: <https://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/1573>. Date accessed: 27 dec. 2025.

Citation Formats

Issue

Vol 10 (2025): (Special Issue): Journal of Advanced Research in Applied Mathematics and Statistics

Section

Research Article

Solution of the Exponential Diophantine Equation 10ð’™ âˆ’ðŸðŸ—ð’š = ð’›ðŸ

Abstract

Solution of the Exponential Diophantine Equation 10ð’™ âˆ’ðŸðŸ—ð’š = ð’›ðŸ