Title: Solutions for a Class of the Higher Diophantine Equation
Abstract: We studied the Diophantine equation x 2 +4 n =y 7 .By using the elementary method and algebaic number theroy, we obtain the following concusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 2 6n -1/7 contains some square factors. (ii) Let x be an even number, when n=7k(k≥1) , all integer solutions for the equation are (x,y)=(0,4 k ) ;when n=7k+3, all integer solutions are (x,y)=(±2 7k+3 ,2 2k+1 ); when n≡1,2,4,5,6 the equation has no integer solution.
Publication Year: 2013
Publication Date: 2013-07-01
Language: en
Type: article
Indexed In: ['crossref']
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