MathDB
Nice sequence

Source: IMO Shortlist 1994, N6

March 29, 2005
modular arithmeticnumber theoryInteger sequencerecurrence relationDivisibilityIMO ShortlistKazakhstan NMO 2022 p6

Problem Statement

Define the sequence a1,a2,a3,... a_1, a_2, a_3, ... as follows. a1 a_1 and a2 a_2 are coprime positive integers and a_{n \plus{} 2} \equal{} a_{n \plus{} 1}a_n \plus{} 1. Show that for every m>1 m > 1 there is an n>m n > m such that amm a_m^m divides ann a_n^n. Is it true that a1 a_1 must divide ann a_n^n for some n>1 n > 1?
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