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2018 Indonesia MO
1
1
Part of
2018 Indonesia MO
Problems
(1)
2n+1 and an+1 are relatively prime
Source: Indonesian National Science Olympiad 2018, Mathematics P1
7/6/2018
Let
a
a
a
be a positive integer such that
gcd
(
a
n
+
1
,
2
n
+
1
)
=
1
\gcd(an+1, 2n+1) = 1
g
cd
(
an
+
1
,
2
n
+
1
)
=
1
for all integer
n
n
n
.a) Prove that
gcd
(
a
−
2
,
2
n
+
1
)
=
1
\gcd(a-2, 2n+1) = 1
g
cd
(
a
−
2
,
2
n
+
1
)
=
1
for all integer
n
n
n
. b) Find all possible
a
a
a
.
number theory
relatively prime