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phi(n,n+1) powers of two- Serbia Mathematical Olympiad 2011
phi(n,n+1) powers of two- Serbia Mathematical Olympiad 2011
Source:
April 8, 2011
Euler
number theory proposed
number theory
Problem Statement
Let
n
n
n
be an odd positive integer such that both
ϕ
(
n
)
\phi(n)
ϕ
(
n
)
and
ϕ
(
n
+
1
)
\phi (n+1)
ϕ
(
n
+
1
)
are powers of two. Prove
n
+
1
n+1
n
+
1
is power of two or
n
=
5
n=5
n
=
5
.
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