International Journal of Statistics and Applied Mathematics
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International Journal of Statistics and Applied Mathematics

2017, Vol. 2, Issue 5, Part A

Study on certain results of exponential diophantine equations


Author(s): Dr. Sajjad Zahir

Abstract: This paper reveals that 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).

Pages: 22-24 | Views: 663 | Downloads: 24

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How to cite this article:
Dr. Sajjad Zahir. Study on certain results of exponential diophantine equations. Int J Stat Appl Math 2017;2(5):22-24.
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