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National Olympiad First Round
2002 National Olympiad First Round
22
P22 [Number Theory] - Turkish NMO 1st Round - 2002
P22 [Number Theory] - Turkish NMO 1st Round - 2002
Source:
August 10, 2014
modular arithmetic
Problem Statement
If
2
n
2^n
2
n
divides
5
256
−
1
5^{256} - 1
5
256
−
1
, what is the largest possible value of
n
n
n
?
<
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a
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c
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a
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x
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a
)
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8
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x
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b
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10
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c
)
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11
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d
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12
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None of above
<span class='latex-bold'>a)</span>\ 8 \qquad<span class='latex-bold'>b)</span>\ 10 \qquad<span class='latex-bold'>c)</span>\ 11 \qquad<span class='latex-bold'>d)</span>\ 12 \qquad<span class='latex-bold'>e)</span>\ \text{None of above}
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8
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a
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x
−
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′
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b
)
<
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10
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=
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a
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x
−
b
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′
>
c
)
<
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11
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=
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a
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x
−
b
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′
>
d
)
<
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12
<
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a
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=
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a
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x
−
b
o
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d
′
>
e
)
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>
None of above
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