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2000 Harvard-MIT Mathematics Tournament
40
40
Part of
2000 Harvard-MIT Mathematics Tournament
Problems
(1)
2000 Guts #40: Phi function
Source:
10/25/2014
Let
ϕ
(
n
)
\phi(n)
ϕ
(
n
)
denote the number of positive integers less than or equal to
n
n
n
and relatively prime to
n
n
n
. Find all natural numbers
n
n
n
and primes
p
p
p
such that
ϕ
(
n
)
=
ϕ
(
n
p
)
\phi(n)=\phi(np)
ϕ
(
n
)
=
ϕ
(
n
p
)
.
function
number theory
relatively prime