A Note on Two Diophantine Equations 17x + 19y = z2 and 71x + 73y = z2

Authors

  • Julius Fergy T. Rabago Department of Mathematics and Physics, College of Arts and Sciences, Central Luzon State University, Science City of Muñoz 3120, Nueva Ecija, Philippines

DOI:

https://doi.org/10.15415/mjis.2013.21002

Keywords:

Exponential Diophantine equations, Catalan’s conjecture, integer solutions

Abstract

In this short note, we study some Diophantine equations of the form px+qy = z2, where x,y, and z are non-negative integers and, p and q are both primes, p < q, with distance two.

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References

Acu, D. (2007) On a Diophantine equation 2x + 5y = z2, Gen. Math., 15, 145-148.

Mihailescu, P. (2004) Primary cycolotomic units and proof of Catalan’s conjecture, J. Reine Angew. Math., 27, 167-195.

Rabago, J. F. T. (2013) On an Open Problem by B. Sroysang, Konuralp Journal of Mathematics 1, no. 2, 30-32.

Rabago, J. F. T. (2013a) A Note on an Open Problem by B. Sroysang, Sci. Technol. RMUTT J., to appear.

Suvarnamani, A., Singta, A. and Chotchaisthit, S. (2011) On two Diophantine Equations 4x + 7y = z2 and 4x + 11y = z2, Sci. Technol. RMUTT J., 1, 25-28.

Sroysang, B. (2012) More on the Diophantine Equation 8x + 19y = z2, International Journal of Pure and Applied Mathematics, 81, no. 4, 601-604.

Sroysang, B. (2012a) On the Diophantine Equation 3x + 5y = z2, International Journal of Pure and Applied Mathematics, 81, no. 4, 605-608.

Sroysang, B. (2012b) On the Diophantine Equation 31x + 32y = z2, International Journal of Pure and Applied Mathematics, 81, no. 4, 609-612.

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Published

2013-09-06

How to Cite

Julius Fergy T. Rabago. 2013. “A Note on Two Diophantine Equations 17x + 19y = Z2 and 71x + 73y = Z2”. Mathematical Journal of Interdisciplinary Sciences 2 (1):19-24. https://doi.org/10.15415/mjis.2013.21002.

Issue

Vol. 2 No. 1 (2013)

Section

Articles

License

 

Articles in Mathematical Journal of Interdisciplinary Sciences (Math. J. Interdiscip. Sci.) by Chitkara University Publications are Open Access articles that are published with licensed under a Creative Commons Attribution- CC-BY 4.0 International License. Based on a work at https://mjis.chitkara.edu.in. This license permits one to use, remix, tweak and reproduction in any medium, even commercially provided one give credit for the original creation.

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Creative Commons License Mathematical Journal of Interdisciplinary Sciences by Chitkara University Publications is licensed under a Creative Commons Attribution 4.0 International License. Based on a work at https://mjis.chitkara.edu.in
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