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a_1 = b_1 = 1 and a_{n+1} = a_n +b_n, b_{n+1} = a_nb_n, coprime terms

Source: 1999 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

January 27, 2020

number theorynumber theory with sequencesSequencesSequencecoprime

Problem Statement

The sequences

(a_n)

and

(b_n)

are defined by

a_1 = b_1 = 1

and

a_{n+1} = a_n +b_n, b_{n+1} = a_nb_n

for

n = 1,2,...

Show that every two distinct terms of the sequence

(a_n)

are coprime