journal6 ›› 2005, Vol. 26 ›› Issue (1): 1-2.

• Mathematics •     Next Articles

On the Diophantine Equation x3+33m=2Dy2


  1. (1.Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong,China;2.Department of Mathematics,Wuzhou Normal College,Hezhou 542800,Guangxi China)
  • Online:2005-01-15 Published:2012-09-22

Abstract: Let D be a positive odd integer with square free.In this paper,it is proved that if D is not divisible by primes of the form 6k+1 and the equation x3+33m=2Dy2 has positive integer solutions (x,y,m) with gcd (x,y)=1,then D≡1 (mod 4),the prime divisors p of D satisfy p≡11 (mod 12) and the number of prime divisors of D is even.

Key words: exponential Diophantine equation, positive integer solution, solvability

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