1995 AIME Problems/Problem 6
Problem
Let How many positive integer divisors of
are less than
but do not divide
?
Solution
We know that must have
factors by its prime factorization. There are
factors of
that are less than
, because if they form pairs
, then there is one factor per pair that is less than
. There are
factors of
that are less than
itself. These are also factors of
. Therefore, there are
factors of
that do not divide
.
See also
1995 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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