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Problem 2
n is power of 2
n is power of 2
Source:
October 11, 2014
number theory unsolved
number theory
Problem Statement
Let
f
(
n
)
f(n)
f
(
n
)
denote the least positive integer
k
k
k
such that
1
+
2
+
⋯
+
k
1+2+\cdots+k
1
+
2
+
⋯
+
k
is divisible by
n
n
n
. Show that
f
(
n
)
=
2
n
−
1
f(n)=2n-1
f
(
n
)
=
2
n
−
1
if and only if
n
n
n
is a power of
2
2
2
.
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