On the Diophantine equation $$x^2+3^a41^b=y^n $$

On the exponential Diophantine equation $x^2+5^a13^b17^c=2^m y^n$

“…As in Case I, if q is a primitive divisor of L 7 (α, ᾱ), then only possibility is q = 13. If b 1 = 0, then L 7 (α, ᾱ) has no primitive divisors, and hence as in Case I by [6, Table 2], we have (2 (1,19), (3,5), (5,7), (13,3), (14,22). These are not possible as m = 0, 1.…”

“…• (k − 2ε, m, u) = (6, 1, 3), which gives (k, m, u, vd) = (4, 1, 3, 5), (8,1,3,89). The only possibility is (k, m, u, vd) = (4, 1, 3, 5), which yields y = 7.…”

“…There are many results concerning the integer solutions of this equation. We refer to some recent results [3,5,9,10,13,22,25,29].…”

The Primitive-Solutions of Diophantine Equation x^2+pqy^2=z^2, for primes p,q

“…Nowadays, there have been many studies about Diophantine equations. Most of their research is about finding the solutions of a given equation, one of which is the work on the equation by Alan and Zengin [2] where are non-negative integers and are realtively prime. There are many forms of Diophantine equations with various variables defined.…”

Solutions to a Lebesgue–nagell Equation

“…Cohn [10] and Bugeaud et al [7] studied (1.1) for λ in the range 1 ≤ λ ≤ 100 and others studied (1.1) when λ is a perfect power (see [2][3][4]17]). Many others studied (1.1) when the set of prime factors of λ is fixed (see [1,8,9,11,12,[14][15][16]18]). For a comprehensive survey of equation (1.1) and its generalisations, see Le and Soydan [13] with over 350 references.…”