Year: 2015
Type: article
Abstract: 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 8 (x) + p (y) = z (2) 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) = (2 (q) - 1, (1/3)(q + 2), 2, 2 (q) + 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).
Source: The Scientific World JOURNAL
DOI: 10.1155/2015/306590
Authors: Lan Qi, Xiaoxue Li
Institutions: Yulin University, Northwest University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $860
Award: G1764318812
OpenAlex ID: W1492620247