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《Journal of Chongqing Normal University(Natural Science)》 2012-02
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On the Diophantine Equation x~3+27=139y~2

XIONG Chuan,LUO Ming(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)  
By using the elementary method of recurrent sequence,congruent formula and quadratic residue,the authors prove that the diophantine equation x3+27=139y2 has only the integer solutions(x,y)=(-3,0),(13,±4).In the process of proving the conclusion,the authors also prove that the diophantine equation x3+1=417y2 has only the integer solution(x,y)=(-1,0),and then give all integer solutions of x3+27=139y2.
【CateGory Index】: O156
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