International Mathematics Competition
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2019

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IMC 2019
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IMC2019: Day 1, Problem 4

Problem 4. Define the sequence \(\displaystyle a_0,a_1,\ldots\) of numbers by the following recurrence:

\(\displaystyle a_0=1, \quad a_1=2, \quad (n+3)a_{n+2}=(6n+9)a_{n+1}- na_n \quad \text{for \(\displaystyle n\ge 0\).} \)

Prove that all terms of this sequence are integers.

Proposed by Khakimboy Egamberganov, ICTP, Italy

        

 

IMC
2019

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