MathDB

Let

S

be the set of positive integer divisors of

20^9.

Three numbers are chosen independently and at random from the set

S

and labeled

a_1,a_2,

and

a_3

in the order they are chosen. The probability that both

a_1

divides

a_2

and

a_2

divides

a_3

\frac mn,

where

m

and

n

are relatively prime positive integers. Find

m.

Problem Statement