1988 AIME Problems/Problem 5
From AoPSWiki
Problem
Let 
, in lowest terms, be the probability that a randomly chosen positive divisor of 
is an integer multiple of 
. Find 
.
Solution
, so it has 
factors. Out of these, we only want those factors of which are divisible by ; it is easy to draw a bijection to the number of factors that 
has, which is 
. Our probability is 
, and 
.
See also
| 1988 AIME (Problems • Resources) | ||
| Preceded by Problem 4 | Followed by Problem 6 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
