Results 91 to 100 of about 20,685 (194)

On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]

Ramanujan J, 2021
Ddamulira M, Luca F.
europepmc   +1 more source

Positive solutions of the diophantine equation

International Journal of Mathematics and Mathematical Sciences, 1982
Integral solutions of x3+λy+1−xyz=0 are observed for all integral λ. For λ=2 the 13 solutions of the equation in positive integers are determined. Solutions of the equation in positive integers were previously determined for the case λ=1.
W. R. Utz
doaj   +1 more source

From Diophantian Equations to Matrix Equations (Iv) - Diophantian Equations of Higher Degree [PDF]

Educaţia 21
In the context of training and developing the skills of teachers, students and children to solve exercises and problems in Mathematics, in this paper we propose to continue the steps started in the first three papers with the same generic title and ...
Teodor Dumitru Vălcan
doaj   +1 more source

Two exponential Diophantine equations [PDF]

Glasgow Mathematical Journal, 1997
In [3], two open problems were whether either of the diophantine equationswith n ∈ Z and f a prime number, is solvable if ω > 3 and 3 √ ω, but in this paper we allow f to be any (rational) integer and also 3 | ω. Equations of this form and more general ones can effectively be solved [5] with an advanced method based on analytical results, but the ...
openaire   +1 more source

All solutions of consecutive natural numbers sum equation and their closed forms

Al-Jabar
Purpose: This study aims to find a closed-form solution for all ordered pairs of natural numbers (?,?) satisfying the consecutive natural number sum equation 1 + 2 + ⋯ + ? sama dengan (? + 1) + (? + 2) + ⋯ + ?. This research contributes to number theory,
Sofihara Al Hazmy, Cahya Alkahfi, Muhamad Syazali, Fulkan Kafilah Al Husein   +3 more
doaj   +1 more source

On the Diophantine equation x3=dy2±q6

International Journal of Mathematics and Mathematical Sciences, 2001
Let q>3 denote an odd prime and d a positive integer without any prime factor p≡1(mod3). In this paper, we have proved that if (x,q)=1, then x3=dy2±q6 has exactly two solutions provided q≢±1(mod24).
Fadwa S. Abu Muriefah
doaj   +1 more source

Is there a computable upper bound for the height of a solution of a Diophantine equation with a unique solution in positive integers?

Open Computer Science, 2017
Let Bn = {xi · xj = xk : i, j, k ∈ {1, . . . , n}} ∪ {xi + 1 = xk : i, k ∈ {1, . . . , n}} denote the system of equations in the variables x1, . . . , xn. For a positive integer n, let _(n) denote the smallest positive integer b such that for each system
Tyszka Apoloniusz
doaj   +1 more source

A Diophantine system

International Journal of Mathematics and Mathematical Sciences, 1986
It is shown how to find all integers a,b such that a+b, a2+b2 and a3+b3 are simultaneously perfect squares.
Andrew Bremner
doaj   +1 more source

A Survey on the ternary purely exponential diophantine equation ax + by = cz [PDF]

Surveys in Mathematics and its Applications, 2019
Let a, b, c be fixed coprime positive integers with min(a,b,c)>1. In this survey, we consider some unsolved problems and related works concerning the positive integer solutions (x,y,z) of the ternary purely exponential diophantine equation ax + by = cz.
Maohua Le, Reese Scott, Robert Styer
doaj  

UHRMS Formula Assignment: Diophantine-Based Recalibration Yields Lorentzian Mass Error Distribution as the Limiting Factor. [PDF]

J Am Soc Mass Spectrom
Safaridehkohneh N, Ott A.
europepmc   +1 more source