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11
2016 Guts #11
2016 Guts #11
Source:
December 24, 2016
Problem Statement
Define
ϕ
!
(
n
)
\phi^!(n)
ϕ
!
(
n
)
as the product of all positive integers less than or equal to
n
n
n
and relatively prime to
n
n
n
. Compute the remainder when
∑
2
≤
n
≤
50
gcd
(
n
,
50
)
=
1
ϕ
!
(
n
)
\sum_{\substack{2 \le n \le 50 \\ \gcd(n,50)=1}} \phi^!(n)
2
≤
n
≤
50
g
c
d
(
n
,
50
)
=
1
∑
ϕ
!
(
n
)
is divided by
50
50
50
.
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