Mock AIME 5 2005-2006 Problems/Problem 1
Problem
Suppose is a positive integer. Let
be the sum of the distinct positive prime divisors of
less than
(e.g.
and
). Evaluate the remainder when
is divided by
.
Solution
So all of the prime numbers less than are
and
. So we just need to find the number of numbers that are divisible by
, the number of numbers divisible by
, etc.
So we compute
Our desired answer then is
See also
Mock AIME 5 2005-2006 (Problems, Source) | ||
Preceded by First Question |
Followed by Problem 2 | |
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