MathDB

(0_x, 1_y, 2_z)

-string is an infinite ternary string such that:

[*] If there is a

0

in position

i

then there is a

1

in position

i + x

,
[*] if there is a

1

in position

j

then there is a

2

in position

j + y

,
[*] if there is a

2

in position

k

then there is a

0

in position

k + z

.

For how many ordered triples of positive integers

(x, y, z)

with

x, y, z \leq 100

does there exist

(0_x, 1_y, 2_z)

-string?

Problem Statement