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a_{n+2}=a_n(a_{n+1}+1) then (a_n)^n |a_{a_n}

Source: Saint Petersburg MO 2020 Grade 11 Problem 6

May 7, 2020
number theory

Problem Statement

The sequence ana_n is given as a_1=1, a_2=2 \;\;\; \text{and} \;\;\;\; a_{n+2}=a_n(a_{n+1}+1)   \forall n\geq 1 Prove that aana_{a_n} is divisible by (an)n(a_n)^n for n≥100n\geq 100.
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