On the Diophantine Equation (4^n)^x − P^y = Z^2-Reference-Cited by-同舟云学术

On the Diophantine Equation (4^n)^x − P^y = Z^2

Published:2020-06-16 Issue: Volume:19 Page:349-352
ISSN:1109-2769
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Elshahed Amr¹,Kamarulhaili Hailiza¹

Affiliation:

1. Universiti Sains Malaysia, School of Mathematical Sciences, Pulau Pinang, MALAYSIA

Abstract

In this paper, the Diophantine equation (4n ) x − p y = z 2 , where p is an odd prime, n ∈ Z + and x, y, z are non-negative integers, has been investigated to show that the solutions are given by {(x, y, z, p)} = {(k, 1, 2 nk − 1, 2 nk+1 − 1)} ∪ {(0, 0, 0, p)}.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference15 articles.

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3. Mihailescu, Preda. ”Primary cyclotomic unitsand a proof of Catalan’s conjecture.” JournalFur die reine und angewandte Mathematik 572(2004): 167-196.

4. Sroysang, Banyat. ”On the Diophantine equation7x+ 8y=z2.” International Journal of Pure and Applied Mathematics 84.1 (2013): 111-114.

5. Sroysang, Banyat. ”More on the Diophantineequation3x+ 85y=z2.” International Journal of Pure and Applied Mathematics 91.1 (2014):131-134.

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