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《Journal of Anhui University(Natural Sciences)》 2008-01
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On the diuphantine equation x~3±1=py~2

MU Shan-zhi1,DAI Xi-min2(1.Department of Foundation Course,Jiangsu Teachers College of Technology,Changzhou 213001,China;2.School of Sciences,Hefei University of Technology,Hefei 230009,China)  
In the paper,we have proved the following theorem:(1) the Diuphantine equations x+1=3py21,x2-x+1=3y22,(y1,y2)=1,y10,y20,where p was an odd prime number,has no positive integer solution x,p,y1,y2.(2) the Diuphantine equation x3+1=py2,where p≡-1(mod 3) was an odd prime number,has only integer solution(x,y)=(-1,0).(3) the Diuphantine equation x3-1=py2,where p≡-1(mod 3) was an odd prime number,has only integer solution(x,y)=(1,0).
【CateGory Index】: O156.7
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