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sequence infinitely

Source: Laurentiu Panaitopol, Romania, TST 1992

August 10, 2005

algebra proposedalgebra

Problem Statement

Let

(a_{n})_{n\geq 1}

and

(b_{n})_{n\geq 1}

be the sequence of positive integers defined by

a_{n+1}=na_{n}+1

and

b_{n+1}=nb_{n}-1

for

n\geq 1

. Show that the two sequence cannot have infinitely many common terms. Laurentiu Panaitopol