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Turkey Contests
National Olympiad First Round
2000 National Olympiad First Round
14
Turkey NMO 2000 1st Round - P14 (Number Theory)
Turkey NMO 2000 1st Round - P14 (Number Theory)
Source:
July 25, 2012
modular arithmetic
Problem Statement
What is the last two digits of the decimal representation of
9
8
7
⋅
⋅
⋅
2
9^{8^{7^{\cdot^{\cdot^{\cdot^{2}}}}}}
9
8
7
⋅
⋅
⋅
2
?
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A
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81
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B
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61
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C
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41
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D
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21
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01
<span class='latex-bold'>(A)</span>\ 81 \qquad<span class='latex-bold'>(B)</span>\ 61 \qquad<span class='latex-bold'>(C)</span>\ 41 \qquad<span class='latex-bold'>(D)</span>\ 21 \qquad<span class='latex-bold'>(E)</span>\ 01
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81
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61
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41
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21
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01
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