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2012 Hanoi Open Mathematics Competitions
11
Q11 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Q11 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Source:
June 10, 2012
modular arithmetic
greatest common divisor
Problem Statement
Q11. Let be given a sequense
a
1
=
5
,
a
2
=
8
a_1=5, \; a_2=8
a
1
=
5
,
a
2
=
8
and
a
n
+
1
=
a
n
+
3
a
n
−
1
,
n
=
1
,
2
,
3
,
.
.
.
a_{n+1}=a_n+3a_{n-1}, \qquad n=1,2,3,...
a
n
+
1
=
a
n
+
3
a
n
−
1
,
n
=
1
,
2
,
3
,
...
Calculate the greatest common divisor of
a
2011
a_{2011}
a
2011
and
a
2012
a_{2012}
a
2012
.
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