journal6 ›› 2007, Vol. 28 ›› Issue (1): 14-15.

• Mathematics • Previous Articles     Next Articles

Primitive Solutions of the Diophantine Euqation xd(n)+yd(n)=zφ(n)


  1. (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China)
  • Online:2007-01-25 Published:2012-06-19

Abstract: Let n be a positive integer,and let d(n) and  φ(n) denote the divisor function and Euler’s totient function respectively.Let p be an odd prime.It is proved that if n=1,2,4,or p,then the equation xd(n)+yd(n)=zφ(n) has infinitely many primitive solutions (x,y,z);if n≠1,2,4 p  or p2,then the equation has no primitive solution (x,y,z).

Key words: higher Diophantine equation;primitive solution;divisor function;Euler&rsquo, s totient function

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