arXiv:2001.09617v1 [math.NT] 27 Jan 2020 Page 1 arXiv:2001.09617v1 [math.NT] 27 Jan
2020 A BRIEF SURVEY ON THE GENERALIZED LEBESGUE-RAMANUJAN-NAGELL …

Let 2≤ p< 100 be a rational prime and consider equation (3) in the title in integer unknowns
x, y, n, k with x> 0, y> 1, n≥ 3 prime, k≥ 0 and gcd (x, y)= 1. Under the above conditions we …

Let q be an odd prime such that qt+ 1= 2cs, where c, t are positive integers and s= 1, 2. We
show that the Diophantine equation x2+ qm= cn has only the positive integer solution (x, m …

On the exponential Diophantine equation $$x^{2}+2^{a}p^{b}=y^{n}$$ | SpringerLink Skip to
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Let d> 0 be a squarefree integer and denote by h= h (− d) the class number of the imaginary
quadratic field. It is well known (see eg [25]) that for a given positive integer N there are only …

Let c≥ 2 be a positive integer. Terai ['A note on the Diophantine equation x2+ qm= cn', Bull.
Aust. Math. Soc. 90 (2014), 20–27] conjectured that the exponential Diophantine equation …

Let q be an odd prime. Let c>1 and t be positive integers such that q^t+1=2c^2. Using
elementary method and a result due to Ljunggren concerning the Diophantine equation x^n …

On generalized Lebesgue-Ramanujan-Nagell equations Page 1 DOI: 10.2478/auom-2014-0006
An. St. Univ. Ovidius Constanta Vol. 22(1),2014, 51–71 On generalized Lebesgue-Ramanujan-Nagell …

On the Diophantine equation $$x^2+3^a41^b=y^n $$ | SpringerLink Skip to main content
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THE EXPONENTIAL LEBESGUE–NAGELL EQUATION X2+ P2m = Yn 1. Introduction Page 1
Periodica Mathematica Hungarica Vol. 67 (2), 2013, pp. 231–242 DOI: 10.1007/s10998-013-3044-7 …