On two diophantine equations 4x + 7y = z2 and 4x + 11y = z2

Article Sidebar

PDF
Published: Aug 23, 2011
Keywords:
exponential diophantine equations

Main Article Content

Alongkot Suvarnamani
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Akarate Singta
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Somchit Chotchaisthit
Faculty of Science, Khon Kaen University

Abstract

In this paper, we show that diophantine equations 4x + 7y = z2 and 4x + 11y = z2 have no solution in non-negative integer.


2000 Mathematics Subject Classication : 11D61

Article Details

How to Cite
1.
Suvarnamani A, Singta A, Chotchaisthit S. On two diophantine equations 4x + 7y = z2 and 4x + 11y = z2. Prog Appl Sci Tech. [Internet]. 2011 Aug. 23 [cited 2024 Apr. 28];1(1):25-8. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/243265
Issue
Vol. 1 No. 1 (2011): August
Section
Mathematics and Applied Statistics

References

D. Acu, On a diophantine equation 2x+5y = z2, General Mathematics, Vol.15, No. 4 (2007), 145-148.

M.B. David, Elementary Number Theory, 6th ed., McGraw-Hill, Singapore, 2007.

H.R. Kenneth, Elementary Number Theory and its Application, 4th ed., Addison Wesley Longman, Inc., 2000.

P. Mihailescu, Primary cyclotomic units and a proof of Catalan's conjecture, J. Reine Angew. Math., 572, 167-195 (2004).

L.J. Mordell, Diophantine Equations, Academic Press, New York, 1969.

J. Sandor, On a diophantine equation 3x + 3y = 6z , Geometric theorems, Diophantine equations, and arithmetric functions, American Research Press Rehobot 4, 2002, 89-90.

J. Sandor, On a diophantine equation 4x +18y = 22z, Geometric theorems, Diophantine equations, and arithmetric functions, American Research Press Rehobot 4, 2002, 91-92.

W. Sierpinski, Elementary Theory of Numbers , Warszawa, 1964.

J.H. Silverman, A Friendly Introduction to Number Theory, 2nd ed., Prentice-Hall, Inc., New Jersey, 2001.