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The Diophantine Equation 8x + py = z2
Open accessAbstract
Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p ≡ ±3(mod 8), then the equation 8x + py = z2 has no positive integer solutions (x, y, z); (ii) if p ≡ 7(mod 8), then the equation has only the solutions (p, x, y, z) = (2q − 1, (1/3)(q + 2), 2, 2q + 1), where q is an odd prime with q ≡ 1(mod 3); (iii) if p ≡ 1(mod 8) and p ≠ 17, then the equation has at most two positive integer solutions (x, y, z).
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Research works printed but not linked: 8
- Sroysang B., 2012, More on the diophantine equation 8 x + 19 y = z 2, International Journal of Pure and Applied Mathematics, 81, 601
- 10.12732/ijpam.v90i1.9 · doi:10.12732/ijpam.v90i1.9
- Rabago J. F. T., 2013, On an open problem by B. Sroysang, Konuralp Journal of Mathematics, 1, 30
- Hua L. G., 1979, An Introduction to Number Theory
- Mordell L. J., 1969, Diophantine Equations
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- 10.4064/aa-60-2-149-167 · doi:10.4064/aa-60-2-149-167
- 10.1515/crll.2004.048 · DOI
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Metadata
- Authors
- Qi, L., & Li, X.
- Venue
- The Scientific World Journal
- Publisher
- Wiley
- Published
- 2015-01
- Volume
- 2015
- Issue
- 1
- Pages
- 306590-306590
- ISSN
- 1537-744X (ISSN-L)
- 2356-6140
- OpenAlex
- W1492620247
- Cited by
- 671
- References
- 0
- FWCI
- 148.66
- Type
- journal article
- Language
- en
- Open access
- gold
- Funders
- National Natural Science Foundation of China (11371291)
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