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9
2004 Algebra #9
2004 Algebra #9
Source:
December 26, 2011
number theory
greatest common divisor
modular arithmetic
Problem Statement
A sequence of positive integers is defined by
a
0
=
1
a_0=1
a
0
=
1
and
a
n
+
1
=
a
n
2
+
1
a_{n+1}=a_n^2+1
a
n
+
1
=
a
n
2
+
1
for each
n
≥
0
n\ge0
n
≥
0
. Find
gcd
(
a
999
,
a
2004
)
\text{gcd}(a_{999},a_{2004})
gcd
(
a
999
,
a
2004
)
.
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