Open Access
Translator Disclaimer
May 2009 A Note on the Diophantine Equation $lx^3 - kx^2 + kx - l = y^2$: The Cases $k=3l \pm 1$
Konstantine Zelator
Missouri J. Math. Sci. 21(2): 136-140 (May 2009). DOI: 10.35834/mjms/1316027246

Abstract

In this work, we investigate the Diophantine equation $lx^3-kx^2+kx-l = y^2$ where $k$ and $l$ are positive integers. The two results are Theorems 1.1 and 1.2. The first theorem states that if $k=3l-1$ and $l = \rho^2$, the above equation has a unique integer solution, namely $(x,y) = (1,0)$. The second theorem says that if $k=3l+1$ and $l\equiv 0,1,4,5,7 \pmod 8$ the above equation also has a unique solution, the pair $(x,y) = (1,0)$.

Citation

Download Citation

Konstantine Zelator. "A Note on the Diophantine Equation $lx^3 - kx^2 + kx - l = y^2$: The Cases $k=3l \pm 1$." Missouri J. Math. Sci. 21 (2) 136 - 140, May 2009. https://doi.org/10.35834/mjms/1316027246

Information

Published: May 2009
First available in Project Euclid: 14 September 2011

zbMATH: 1187.11009
MathSciNet: MR2529016
Digital Object Identifier: 10.35834/mjms/1316027246

Subjects:
Primary: 11DXX

Rights: Copyright © 2009 Central Missouri State University, Department of Mathematics and Computer Science

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.21 • No. 2 • May 2009
Back to Top