journal6 ›› 2006, Vol. 27 ›› Issue (6): 9-10.

• Mathematics • Previous Articles     Next Articles

Integral Part of Powers of Real Quadratic Units


  1. (Department of Mathematics,Zhanjiang Normal College,Zhanjiang 524048,Guangdong China)
  • Online:2006-11-25 Published:2012-06-28

Abstract: Let D be a positive integer which is not a perfect square,and let α=(u+v〖KF(〗D〖KF)〗)2,where (u,v) is positive integer solution of the Pell equation u2-Dv2=1.It is proved that,for any positive integer n,[αn] is an odd integer and [αn]+3 is a perfect square,where [αn] is the integral part of αn.

Key words: real quadratic field, unit, power, integral part

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