In this paper, we study on the exponential Diophantine equations: nx+ 24y= z2, for n≡ 5 or 7
(mod 8). We show that 5x+ 24y= z2 has a unique positive integral solution (2, 1, 7). Further …

In this paper, we study the Diophantine equation (p+ n)^ x+ p^ y= z^ 2, where p, p+ n are
prime numbers and n is a positive integer such that n equiv mod 4. In case p= 3 and n= 4 …

This paper investigates the Diophantine equation pr+(p+ 1) s= z2 Where p> 3, s≥ 3, z is an
even integer. The focus of the study is to establish rigorous results concerning the existence …

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 …

On the exponential Diophantine equation (p + 2) + (2p + 1) = z2, where p, p + 2 and 2p + 1 are
primes 1 Introduction Page 1 International Journal of Mathematics and Computer Science …

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 …

Objectives: The specified problem addressed here is the existence and nonexistence of
Exponential Diophantine triangles over triangular numbers (tn, n∈ N). Methods: An …

In this paper, we study the Diophantine equation $(p+ 4n)^ x+ p^ y= z^ 2, $ where $ n $ is a
non-negative integer and $ p, p+ 4n $ are prime numbers such that $ p\equiv 7\pmod {12} …

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) …