Results 21 to 30 of about 3,148,152 (262)
Separable Diophantine Equations [PDF]
Transactions of the American Mathematical Society, 1945 Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
openaire +2 more sources
NOTE ON THE DIOPHANTINE EQUATION [PDF]
, 2000 NOTE ON THE DIOPHANTINE ...
Atanassov, Krassimir +2 more
core +1 more source
Some experiments with Ramanujan-Nagell type Diophantine equations [PDF]
, 2014 Stiller proved that the Diophantine equation $x^2+119=15\cdot 2^{n}$ has exactly six solutions in positive integers. Motivated by this result we are interested in constructions of Diophantine equations of Ramanujan-Nagell type $x^2=Ak^{n}+B$ with many ...
Ulas, Maciej
core +3 more sources
On the exponential Diophantine equation Pxn+Pxn+1=Pm
Turkish Journal of Mathematics, 2019 In this paper, we find all the solutions of the title Diophantine equation in nonnegative integer variables $(m, n, x)$, where $P_k$ is the $k$th term of the Pell sequence.
S. Rihane +3 more
semanticscholar +1 more source
On the Diophantine equations $x^2-Dy^2=-1$ and $x^2-Dy^2=4$
AIMS Mathematics, 2019 In this paper, using only the Störmer theorem and its generalizations on Pell's equation and fundamental properties of Lehmer sequence and the associated Lehmer sequence, we discuss the Diophantine equations $x^2-Dy^2=-1$ and $x^2-Dy^2=4$.
Bingzhou Chen, Jiagui Luo
doaj +1 more source
Journal of Physics: Conference Series, 2019 This research may provide the solutions (if any) from the Non-linear Diophantine equation (7k — 1)x + (7k )y = Z2.There are 3 possibilities to determine the solutions from the Non-linear Diophantine equation: single solution, multiple solutions, and no ...
R. Rahmawati +3 more
semanticscholar +1 more source
An Introduction to Refined Neutrosophic Number Theory [PDF]
Neutrosophic Sets and Systems, 2021 Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell's equation
Mohammad Abobala, Muritala Ibrahim
doaj +1 more source
THE AVERAGE SMARANDACHE FUNCTION [PDF]
, 1995 Presenting an application to a diophantine equation.
Luca, Florian
core +1 more source
Multiplicative Diophantine equations
Journal of Number Theory, 1992 The solution of the diophantine equation \(\prod_{i=1}^ n x_ i= \prod_{i=1}^ n y_ i\) is given in terms of \(n^ 2\) parameters (Bell's theorem) [cf. the first author, Proc. Ramanujan Cent. Int. Conf., Annamalainagar/India 1987, RMS Publ. 1, 141-146 (1988; Zbl 0696.10014)].
Srinivasa Rao, K. +2 more
openaire +1 more source
On the Diophantine Equation 3x + p5y = z2
Walailak Journal of Science and Technology, 2019 In this paper, we present new series of solutions of the Diophantine equation 3x + p5y = z2 where p is a prime number and x; y and z are nonnegative integers using elementary techniques. Moreover, the equation has no solution if p is equivalent to 5 or 7
K. Laipaporn +2 more
semanticscholar +1 more source