journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-2225 An exponential Diophantine equation x2 + 3a 73b = yn Muthuvel S. Department of Mathematics, Faculty of Engineering and Technology, Vadapalani Campus, No. 1, Jawaharlal Nehru Salai, Vadapalani, SRM Institute of Science and Technology, Chennai, Tamil Nadu, 600026, India Venkatraman R. Department of Mathematics, Faculty of Engineering and Technology, Vadapalani Campus, No. 1, Jawaharlal Nehru Salai, Vadapalani, SRM Institute of Science and Technology, Chennai, Tamil Nadu, 600026, India 28 6 2289 2296 16 09 2025

This paper aims to identify all solutions in positive integers x and y (where x, y ≥ 1), with nonnegative exponents a and b, and an integer n ≥ 3, that satisfy the Diophantine equation x2 + 3a 73b = yn under the condition x and y are coprime.

 Integer solution Diophantine equations S-integers Primitive divisor Lucas sequence access open retracted no