Difference between revisions of "Mock AIME 1 2006-2007 Problems/Problem 5"
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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>. | ||
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+ | [[Mock AIME 1 2006-2007]] |
Revision as of 14:57, 24 July 2006
5. 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:
.