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2019 CHMMC (Fall)
7
7
Part of
2019 CHMMC (Fall)
Problems
(1)
2019 Fall Team #7
Source:
4/17/2022
Let
S
S
S
be the set of all positive integers
n
n
n
satisfying the following two conditions:
∙
\bullet
∙
n
n
n
is relatively prime to all positive integers less than or equal to
n
6
\frac{n}{6}
6
n
∙
\bullet
∙
2
n
≡
4
2^n \equiv 4
2
n
≡
4
mod
n
n
n
What is the sum of all numbers in
S
S
S
?
number theory