Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 1"
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== See also == | == See also == |
Revision as of 19:18, 14 November 2016
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 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |