scholarly journals Infinitely many positive solutions of the diophantine equation x2 − kxy + y2 + x = 0

2004 ◽  
Vol 47 (1) ◽  
pp. 115-121 ◽  
Author(s):  
A. Marlewski ◽  
P. Zarzycki
Keyword(s):  
Positive Solutions ◽  
Diophantine Equation

scholarly journals Positive solutions of the diophantine equation

1982 ◽  
Vol 5 (2) ◽  
pp. 311-314 ◽  
Author(s):  
W. R. Utz
Keyword(s):  
Positive Solutions ◽  
Diophantine Equation ◽  
Positive Integers ◽  
Integral Solutions

Integral solutions ofx3+λy+1−xyz=0are observed for all integralλ. Forλ=2the 13 solutions of the equation in positive integers are determined. Solutions of the equation in positive integers were previously determined for the caseλ=1.

scholarly journals A note on the Diophantine Equation x^2-kxy+ky^2+ly=0

Mathematica ◽  
2021 ◽  
Vol 63 (86) (2) ◽  
pp. 151-157
Author(s):  
Sakha A. Alkabouss ◽  
◽  
Boualem Benseba ◽  
Nacira Berbara ◽  
Simon Earp-Lynch ◽  
...  
Keyword(s):  
Positive Solutions ◽  
Diophantine Equation

We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.

scholarly journals On Fixed Points of Iterations Between the Order of Appearance and the Euler Totient Function

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1796
Author(s):  
Štěpán Hubálovský ◽  
Eva Trojovská
Keyword(s):  
Positive Integer ◽  
Fixed Points ◽  
Natural Number ◽  
Positive Solutions ◽  
Diophantine Equation ◽  
Fibonacci Number ◽  
Euler Totient Function

Let Fn be the nth Fibonacci number. The order of appearance z(n) of a natural number n is defined as the smallest positive integer k such that Fk≡0(modn). In this paper, we shall find all positive solutions of the Diophantine equation z(φ(n))=n, where φ is the Euler totient function.

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

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