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2003 All-Russian Olympiad
4
Determine a_2003
Determine a_2003
Source:
November 3, 2010
algebra unsolved
algebra
Problem Statement
A sequence
(
a
n
)
(a_n)
(
a
n
)
is defined as follows:
a
1
=
p
a_1 = p
a
1
=
p
is a prime number with exactly
300
300
300
nonzero digits, and for each
n
≥
1
,
a
n
+
1
n \geq 1, a_{n+1}
n
≥
1
,
a
n
+
1
is the decimal period of
1
/
a
n
1/a_n
1/
a
n
multiplies by
2
2
2
. Determine
a
2003
.
a_{2003}.
a
2003
.
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