Journal of the Ramanujan Mathematical Society
Volume 41, Issue 2, June 2026 pp. 185–192.
On the exponential Diophantine equation cx{2} + p{1}{2m1}
p{2}{2m2} ⋯ p{r}{2mr}
r = 4y{q}
Authors:
Azizul Hoque, Srinivas Kotyada and Usha K. Sangale
Author institution:Department of Mathematics, Gauhati University, Gawahati, Assam 781 014, India.
Summary:
We first extensively investigate the solvability of the Diophantine equation as in the title, where c > 1
is a square-free integer, p{1}, p{2}, …, p{r} are distinct odd primes, and x, y, m{1},m{2}, …, m{r} are unknown positive integers
with gcd(x, y) = 1. We then use this result to describe all the positive integer solutions of some of its variants.
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