广义 Pell数列中的平方类(英文)

Square classes of generalized Pell sequences

设 t是大于 1的整数 ,U ={Uk}k=0 是参数为 t的广义 Pell数列。本文证明了 :如果 t=2 dr2 ,( t+t2 +1 ) d +( t-t2 +1 ) d =4s2 ,其中 d ,r,s是正整数 ,而且 d是无平方因子正奇数 ,则 U恰有一个平方类 {Ud,U2 d};否则 ,U没有平方类。

Let t be a positive integer with t>1, and let U={U k} k=0  be the generalized Pell sequence with parametes t.In this paper, we prove that if t=2dr 2and(t+t 2+1) d+ (t-t 2+1) d=4s 2 ,where d, r, s are positive integers satisfying 2d and d is square free,then U has exactly one square class {U d,U 2d }.Otherwise, U has no square classes.