journal6 ›› 2006, Vol. 27 ›› Issue (3): 7-7.

• Mathematics • Previous Articles     Next Articles

On the Diophantine Equation x3±23m=3Dy2


  1. (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China)
  • Online:2006-05-25 Published:2012-09-11

Abstract: Let m be a positive integer,and D be a positive integer with square free.It is proved that if m>1 and D is not divisible by 3 or primes of the form 6k+1,then the equation x3±23m=3Dy2has no positive integer solutions (x,y) with gcd(x,y)=1.

Key words: cubic Diophantine equation, positive integer solution, existence

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