Results 81 to 90 of about 1,510,077 (175)

A remark on a Diophantine equation of S. S. Pillai

open access: yes
summary:S. S. Pillai proved that for a fixed positive integer $a$, the exponential Diophantine equation $x^y-y^x= a$, $\min (x,y)>1$, has only finitely many solutions in integers $x$ and $y$.
Hoque, Azizul
core   +1 more source

Exploration of Solutions for an Exponential Diophantine Equation px+ (p +1)y= z2

open access: yes, 2021
In this text, the exclusive exponential Diophantine equation px + (p + 1)y= z2such that the sum of integer powers  and  of two consecutive prime numbers engrosses a square is examined or estimating enormous integer solutions by exploiting the ...
et. al., P. Sandhya,
core  

On the solutions of the exponential diophantine equation ax + by = (m2 + 1)z

open access: yes, 2013
Click on the link to view the abstract.Keywords: Exponential Diophantine equation, Terai conjecture, positive integer solution, linear forms in two logarithms, lower bound, primitive divisorQuaestiones Mathematicae 36(2013), 119 ...
Togbe, Alain, Yang, Shichun, He, Bo
core  

On the Exponential Diophantine Equation 7^x − 5^y = z^2

open access: yes
In this paper, we address the exponential Diophantine equation 7x − 5y = z2 , seeking non-negative integer solutions for x, y, and z. Using many congruence theorems and Catalan’s conjecture, we prove the existence of a single solution. Our analysis shows
BUDEE U ZAMAN
core   +1 more source

Selection on X 1 + X 2 + ⋯ + X m via Cartesian product trees. [PDF]

open access: yesPeerJ Comput Sci, 2021
Kreitzberg P   +3 more
europepmc   +1 more source

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