MathDB
Prove that n exists satisfying divisibility

Source:

December 31, 2011
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Let (an)n≥1(a_n )_{n\ge 1} be a sequence of integers that satisfies an=an−1−min(an−2,an−3)a_n = a_{n-1} -\text{min}(a_{n-2} , a_{n-3} ) for all n≥4n \ge 4. Prove that for every positive integer kk, there is an nn such that ana_n is divisible by 3k3^k .
Back to ProblemsView on AoPS