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National and Regional Contests
Turkey Contests
National Olympiad First Round
2008 National Olympiad First Round
14
Turkey NMO 2008 1st Round - P14 (Number Theory)
Turkey NMO 2008 1st Round - P14 (Number Theory)
Source:
August 25, 2012
Euler
modular arithmetic
Problem Statement
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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081
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561
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721
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961
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