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Given two sequences. Show that they have finite common terms

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October 12, 2010
number theory unsolvednumber theory

Problem Statement

Let (an)n≥1(a_n)_{n\ge 1} and (bn)n≥1(b_n)_{n\ge 1} be two sequences of natural numbers such that an+1=nan+1,bn+1=nbn−1a_{n+1} = na_n + 1, b_{n+1} = nb_n - 1 for every n≥1n\ge 1. Show that these two sequences can have only a finite number of terms in common.
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