Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-24T05:15:37.102Z Has data issue: false hasContentIssue false

On an diophantine equation

Published online by Cambridge University Press:  17 April 2009

Florian Luca
Affiliation:
Mathematical Institute, Czech Academy of Sciences, Zitná 25, 115 67 Praha 1, Czech Republic, e-mail: luca@math.cas.cz
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we find all solutions of the diophatine equation x2 + 3m = yn, where (x, y, m, n) are non-negative integers with x ≠ 0 and n ≥ 3.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Arif, S.A. and Muriefah, F.S.A., ‘The diophantine equation x2 + 3m = yn,, Internat, J. Math. Math. Sci. 21 (1998), 619620.CrossRefGoogle Scholar
[2]Arief, S.A. and Muriefah, F.S.A., ‘On a diophantine equation’, Bull. Austal. Math. Soc 57 (1998), 189198.Google Scholar
[3]Bilu, Y., Hanrot, G. and Voutier, P.M., ‘Existence of primitive divisors of Lucas and Lehmer numbers’, (preprint).Google Scholar
[4]Cohn, J.H.E., ‘The diophantine equation x2 + 3 = yn’, Glasgow Math. J 35 (1993), 203206.CrossRefGoogle Scholar
[5]Cohn, J.H.E., ‘The diophantine equation x2 + c = yn’, Acta. Arith 65 (1993), 367381.CrossRefGoogle Scholar
[6]Ko, Chao, ‘On the diophantine equation x2 = yn + 1, xy ≠ 0’, Sci. Sinica 14 (1965), 457460.Google Scholar
[7]Lebesgue, V.A., ‘Sur l'impossibilité en nombres entiers de l'equation xm = y2 + 11’, Nouv. Annal. des Math 9 (1850), 178181.Google Scholar