IJPAM: Volume 107, No. 4 (2016)
School of Mathematical Sciences
Universiti Sains Malaysia
11800, Penang, MALAYSIA
Abstract. This paper solves the Diophantine equation nontrivially in the case of where is prime and . The parametric solutions are formulated using number theory theorems, especially those concerning divisibility of integers, linear Diophantine equations, properties of prime numbers, and properties of congruence. There exist infinitely many nontrivial integral solutions to this Diophantine equation, where the parametric solutions found solve completely for different values of and in the case of .
Received: February 23, 2016
AMS Subject Classification: 11D41
Key Words and Phrases: Diophantine equation, congruence, septic degree
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DOI: 10.12732/ijpam.v107i4.23 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 1063 - 1072
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