Putnam 1956 B6

Given $T_1 =2, T_{n+1}= T_{n}^{2} -T_n +1$ for $n>0.$ Prove:

(i) If $m \ne n,$ $T_m$ and $T_n$ have no common factor greater than $1.$ (ii) $\sum_{i=1}^{\infty} \frac{1}{T_i }=1.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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