二次域Q(7^(1/2))的单位给出的Pronic数及相关的不定方程问题

Problems of Pronic Numbers Given by the Units of Quadratic Field Q(7^(1/2)) and Related Diophantine Equations

研究了二次域Q(7^(1/2))中单位V_n+U_n7^(1/2)=(8+3 7^(1/2))~n所给出的两个递归数列{V_n},{U_n}中的Pronic数问题,找到了{V_n},{U_n}中的所有的Pronic数.作为应用,给出了与其相关的两个不定方程的整数解.

This paper researches the problems of Pronic numbers in two recurrent sequences { Un } and {Vn }, which are given by the units Vn ＋ Un √7= （8 ＋ 3√7）^n of quadratic field Q（√7） and finds out all Pronic numbers in {Vn} and {Un}. As applications, all integer solutions of two related Diophantine equations are obtained .