MathDB

Three distinct integers

a_1

a_2

a_3

between

1

and

21

, inclusive, are selected uniformly at random. The probability that the greatest common factor of

a_i-a_j

and

21

7

for some positive integers

i

and

j

, where

1 \le i \ne j \le3

, can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Compute

m + n

Problem Statement