Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 5"
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− | + | Let <math>p</math> be a prime and <math>f(n)</math> satisfy <math>0\le f(n) <p</math> for all integers <math>n</math>. <math>\lfloor x\rfloor</math> is the greatest integer less than or equal to <math>x</math>. If for fixed <math>n</math>, there exists an integer <math>0\le y < p</math> such that: | |
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then <math>f(n)=y</math>. If there is no such <math>y</math>, then <math>f(n)=0</math>. If <math>p=11</math>, find the sum: <math>f(1)+f(2)+...+f(p^{2}-1)+f(p^{2})</math>. | then <math>f(n)=y</math>. If there is no such <math>y</math>, then <math>f(n)=0</math>. If <math>p=11</math>, find the sum: <math>f(1)+f(2)+...+f(p^{2}-1)+f(p^{2})</math>. | ||
− | [[Mock AIME 1 2006-2007]] | + | ==Solution== |
+ | {{solution}} | ||
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+ | ---- | ||
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+ | *[[Mock AIME 1 2006-2007/Problem 4 | Previous Problem]] | ||
+ | |||
+ | *[[Mock AIME 1 2006-2007/Problem 6 | Next Problem]] | ||
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+ | *[[Mock AIME 1 2006-2007]] |
Revision as of 17:27, 17 August 2006
Let be a prime and
satisfy
for all integers
.
is the greatest integer less than or equal to
. If for fixed
, there exists an integer
such that:
then . If there is no such
, then
. If
, find the sum:
.
Solution
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