Abstract
We studied the Diophantine equation x2+4n=y11. By using the elementary method and algebraic number theory, we obtain the following conclusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 210n-1/11 contains some square factors. (ii) Let x be an even number, when n=11k(k≥1), all integer solutions for the equation are(x,y)=(0,4k) ; whenn=11k+5(k≥0) , all integer solutions are(x,y)=(±211k+5,22k+1); when n≡1,2,3,4,6,7,8,9,10 the equation has no integer solution.
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