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2016 CNMO Grade 11 P3

Source: 2016 China Northern MO Grade 11, Problem 3

February 25, 2020
number theoryfunctionEuler

Problem Statement

m(m>1)m(m>1) is an intenger, define (an)(a_n): a0=m,an=φ(an−1)a_0=m,a_{n}=\varphi(a_{n-1}) for all positive intenger nn. If for all nonnegative intenger kk, ak+1∣aka_{k+1}\mid a_k, find all mm that is not larger than 20162016. Note: φ(n)\varphi(n) means Euler Function.
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