Amr Elshahed, Hailiza Kamarulhaili, "On the Diophantine Equation (4^n)^x − P^y = Z^2," WSEAS Transactions on Mathematics, vol. 19, pp. 349-352, 2020, DOI:10.37394/23206.2020.19.35
Amr Elshahed, Hailiza Kamarulhaili. On the Diophantine Equation (4^n)^x − P^y = Z^2.
WSEAS Transactions on Mathematics. 2020;19:349-352. 10.37394/23206.2020.19.35
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 19, 2020
On the Diophantine Equation (4^n)^x − P^y = Z^2
Authors: ,
Abstract: In this paper, the Diophantine equation $$(4^n)^x − p^y = z^2.$$, 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 $${(x, y, z, p)} = {(k, 1, 2^{nk} − 1, 2^{nk+1} − 1)} ∪ {(0, 0, 0, p)}.$$
Pages: 349-352 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 19, 2020, Art. #35 DOI: 10.37394/23206.2020.19.35
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