IMO 1984 LL ROM46

Let (an)n\geq1 and (bn)n\geq1 be two sequences of natural numbers

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IMO 1984 LL ROM46

Origin: ROM

Problem

Let (an)n\geq1 and (bn)n\geq1 be two sequences of natural numbers such that an+1 = nan + 1, bn+1 = nbn −1 for every n \geq1. Show that these two sequences can have only a finite number of terms in common.