MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
14
14
Part of
2008 National Olympiad First Round
Problems
(1)
Turkey NMO 2008 1st Round - P14 (Number Theory)
Source:
8/25/2012
What is the last three digits of
4
9
303
⋅
399
3
202
⋅
3
9
606
49^{303}\cdot 3993^{202}\cdot 39^{606}
4
9
303
⋅
399
3
202
⋅
3
9
606
?
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001
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081
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561
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721
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961
<span class='latex-bold'>(A)</span>\ 001 \qquad<span class='latex-bold'>(B)</span>\ 081 \qquad<span class='latex-bold'>(C)</span>\ 561 \qquad<span class='latex-bold'>(D)</span>\ 721 \qquad<span class='latex-bold'>(E)</span>\ 961
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001
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081
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561
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721
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961
Euler
modular arithmetic