The Diophantine equation $ p^ x+ (p+ 2q)^ y= z^ 2$, where $ p $, $ q $ and $ p+ 2q $ are
prime numbers, is studied widely. Many authors give $ q $ as an explicit prime number and …

In this paper, we consider Exponential Diophantine equations of the form pX+(p+ λ+ 1) Y=
Z2 over the set of all positive integers, where p> 3, p+ λ+ 1 and λ are primes with λ being a …

We consider the Diophantine equation (− 1) α p x+(− 1) β (2 k (2 p+ 1)) y= z 2 for Sophie
Germain primes p with α, β∈{0, 1}, α β= 0 and k≥ 0. First, for p= 2, we solve three …

In this paper, for prime pairs p and 2p− 1, we consider the Diophantine equations (− 1)
αpx+(− 1) β (2k (2p− 1)) y= z2 with α, β∈{0, 1}, αβ= 0 and a non-negative integer k. We first …

In this paper, we solve the Diophantine equation ua+ vb= z 2 in the set of non-negative
integers. Here, the base pair (u, v) is any of the prime pairs of the form (u, 4 u+ 1),(u, 4 u+ 3) …

This work studies Diophantine equations of the form AX− BY= Z2. Specifically, we determine
the nonnegative integer solutions (pM, a, b, c) of the exponential Diophantine equation (pM) …

Abstract Let Fk be a Fibonacci number and let Lk be a Lucas number. By applying Catalan's
conjecture and the modular arithmetic method, we solve the exponential Diophantine …

The Complete Set of Non-negative Integer Solutions for the Diophantine Equation (pq) + py =
z2 , where p, q, x, y, z are non-neg Page 1 International Journal of Mathematics and Computer …

We study the Diophantine equation (2p+ 1) x+(2q+ 1) y= z2 where p and q are Sophie
Germain primes. We prove that for p≤ q and p ̸= 2 the solution to this Diophantine …

In this paper, we study Diophantine equations and, where and are primes. We found that all
non-negative integer solutions of the Diophantine equation are of the following and all non …