MathDB

Andrew chooses three (not necessarily distinct) integers

a

b

, and

c

independently and uniformly at random from

\{1,2,3,4,5,6,7\}

. Let

p

be the probability that

abc(a+b+c)

is divisible by

4

. If

p

can be written as

\frac{m}{n}

for relatively prime positive integers

m

and

n

, then compute

m+n

.
Proposed by Andrew Wen

Problem Statement