一类序列的平方数

The Square Numbers of a Class of Sequence

设u_1=1,u_(?)=4,H_n=4u_(n-1)-u_n-2 (n≥3)及v_1=4,v_2=14,v_n=4v_(n-1)-V_n-2(n≥3),本文的主要结果为: 定理1 v_n=x^2仅当n=1,x=±2, v_n=2x^2对任意n均无解。定理2 u_n=x^2仅当n=1,2,x=±1,±2。 u_n=2x^2对任意n均无解。

Let u_1=1, u_2=4, u_n=4u_(n-1)-u_(n-2)(n≥3), and v_1=4, v_2=14, v_n=4v_(n-1)-v_(n-2)(n≥3). In this paper we prove some Theorems as follows. Theorem 1 (A) The equation v_n=x^2 has no integer solutions except n=1, x=±2. (B) The equation v_n=2x^2 has no integer solutions. Theorem 2 (A) The equation u_n=x^2 has no integer solutions except n=1, 2, x=+1, ±2. (B) The equation u_n=2x^2 has no integer solutions