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《Journal of Science of Teachers' College and University》 2008-05
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On the Diophantine equation x~3+1=py~2

YANG YA-lin(Department of Mathematics,Northwest University,Xi'an 710127,China)  
Appling congruence theory,given some sufficient conditions under which the Diophantine equation x3+1=py2has no positive integer solution.Let p be an odd prime,proved that if p=3(24k+19)(24k+20)+1,wherek is a nonnegative integer,then the equation x3+1=py2has no positive integer solution.
【CateGory Index】: O156.7
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