MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1999 National Olympiad First Round
30
30
Part of
1999 National Olympiad First Round
Problems
(1)
Modular Arithmetics
Source: 0
4/21/2009
a
i
∈
{
0
,
1
,
2
,
3
,
4
}
a_{i} \in \left\{0,1,2,3,4\right\}
a
i
∈
{
0
,
1
,
2
,
3
,
4
}
for every
0
≤
i
≤
9
0\le i\le 9
0
≤
i
≤
9
. If 6\sum _{i \equal{} 0}^{9}a_{i} 5^{i} \equiv 1\, \, \left(mod\, 5^{10} \right), a_{9} \equal{} ?
<
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A
)
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C
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D
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3
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E
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4
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4
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(
B
)
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)
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D
)
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3
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>
(
E
)
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4