Solutions for a Class of the Higher Diophantine Equation

Xue Fu Kang

doi:10.4028/www.scientific.net/AMM.729.220

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 729Solutions for a Class of the Higher Diophantine...

Solutions for a Class of the Higher Diophantine Equation

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.