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ASU 268 All Russian MO 1978 x_n=(1+\sqrt(2)+\sqrt(3))^n , limits

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July 11, 2019
analysisalgebraSequence

Problem Statement

Consider a sequence xn=(1+2+3)nx_n=(1+\sqrt2+\sqrt3)^n Each member can be represented as xn=qn+rn2+sn3+tn6x_n=q_n+r_n\sqrt2+s_n\sqrt3+t_n\sqrt6 where qn,rn,sn,tnq_n, r_n, s_n, t_n are integers. Find the limits of the fractions rn/qn,sn/qn,tn/qnr_n/q_n, s_n/q_n, t_n/q_n.
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