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A4

Part of 1964 Putnam

Problems(1)

Putnam 1964 A4

Source: Putnam 1964

3/5/2022
Let pnp_n be a bounded sequence of integers which satisfies the recursion pn=pn−1+pn−2+pn−3pn−4pn−1pn−2+pn−3+pn−4.p_n =\frac{p_{n-1} +p_{n-2} + p_{n-3}p _{n-4}}{p_{n-1} p_{n-2}+ p_{n-3} +p_{n-4}}. Show that the sequence eventually becomes periodic.
Putnamrecurrence relationperiodic