Results 121 to 130 of about 2,597 (231)

Time-varying Feedback Systems Design Via Diophantine Equation Order Reduction [PDF]

, 2007
Diophantine equation plays an important role in the design and synthesis of feedback compensators. Many methods have been developed to solve the Diophantine equation.
Wu, Shr-Hua
core  

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

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

On a Diophantine equation of Erdös

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994
The second lemma is not proved in the quoted paper. It would lead to a polynomial bound in the height of the binary form. Despite this the main results can be true.
openaire   +3 more sources

On the Diophantine equation x2−4pm=±yn [PDF]

, 2012
Let m and n be positive integers and p any odd prime. In this paper we consider the Diophantine equation x2−4pm=±yn in positive integers x and y where (x,y)=1, and we show that under some not very restrictive conditions, this equation has only finitely ...
Abu Muriefah, Fadwa S., AL-Rashed, Amal
core   +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

On Some Diophantine Equations

, 1988
Our purpose is to study a variety of Diophantine equations involving the Smarandache function.
Tuţescu, Lucian, Burton, Emil
openaire   +2 more sources

On the Diophantine Equation CZ2 = X5 + Y5 [PDF]

, 2011
In this work we determine an infinit sequence of different values of C for which the diophantine equation Cz2 = x5 + y5 has no coprime non-trivial ...
Aldén, Erik, Söderlund, Gustaf
core  

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