MathDB
Largest power of $3$ dividing a_101

Source: Kyiv City MO 2021 Round 1, Problem 10.5

December 21, 2023
number theorySequence

Problem Statement

The sequence (an)(a_n) is such that an+1=(an)n+n+1a_{n+1} = (a_n)^n + n + 1 for all positive integers nn, where a1a_1 is some positive integer. Let kk be the greatest power of 33 by which a101a_{101} is divisible. Find all possible values of kk.
Proposed by Kyrylo Holodnov
Back to ProblemsView on AoPS