MathDB

China Mathematical Olympiad 1988 problem6

Source: China Mathematical Olympiad 1988 problem6

November 5, 2013

number theoryrelatively primenumber theory unsolved

Problem Statement

Let

n

(

n\ge 3

) be a natural number. Denote by

f(n)

the least natural number by which

n

is not divisible (e.g.

f(12)=5

). If

f(n)\ge 3

, we may have

f(f(n))

in the same way. Similarly, if

f(f(n))\ge 3

, we may have

f(f(f(n)))

, and so on. If

\underbrace{f(f(\dots f}_{k\text{ times}}(n)\dots ))=2

, we call

k

the “length” of

n

(also we denote by

l_n

the “length” of

n

). For arbitrary natural number

n

(

n\ge 3

), find

l_n

with proof.

Back to Problems View on AoPS