Proceedings of the 2013 International Conference on Advanced Computer Science and Electronics Information (ICACSEI 2013)

Solutions for a Class of the higherDiophantine equation

Yin xia Ran
Corresponding author
Higher Diophantine equation, integer solutions, integer ring, algebraic number theroy
We studied the Diophantine equation x2+4n=y9. 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 28n-1/3 contains some square factors. (ii) Let X be an even number, when n=9k(k 1), all integer solutions for the equation are(x, y)=(0,4k), when n=9k+4(k 0), all integer solutions are (x, y)=(29k+4, 22k+1), when n 1,2,3,5,6,7,8(mod9)the equation has no integer solution.
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