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2017 Canada National Olympiad
2
2
Part of
2017 Canada National Olympiad
Problems
(1)
CMO 2017 P2
Source: Canadian Mathematical Olympiad 2017
3/31/2017
Define a function
f
(
n
)
f(n)
f
(
n
)
from the positive integers to the positive integers such that
f
(
f
(
n
)
)
f(f(n))
f
(
f
(
n
))
is the number of positive integer divisors of
n
n
n
. Prove that if
p
p
p
is a prime, then
f
(
p
)
f(p)
f
(
p
)
is prime.
function
number theory