2015•Applied Mechanics and MaterialsRequires access

Solutions for a Class of the Higher Diophantine Equation

Xue Fu Kang

Abstract

We studied the Diophantine equation . By using the elementary method and algebaic number theroy, we obtain the following concusions: (i) Let be an odd number, one necessary condition which the equation has integer solutions is that contains some square factors. (ii) Let be an even number, when , all integer solutions for the equation are; when , all integer solutions are ; when the equation has no integer solution.

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Key concepts: Diophantine equation, Integer (computer science), Mathematics, Diophantine set, Class (philosophy), Radical of an integer, Legendre's equation, Discrete mathematics