Alphabet: = {0, 1, 2}

Given a string w in :

Assign numerical value to w in base 3 notation, denoted as [w]₃

[]₃ = 0

if w = a_ka_k1 . . . a₁, then

[w]₃ = 3^k1 a_k + 3^k2 a_k1 + . . . + 3² a₃ + 3 a₂ + a₁.

For example [2122]3 = 3³ 2 + 3² 1 + 3 2 + 2 = 71 and [202] = 3² 2 + 3 0 + 2 = 20.

Language A₃ is a subset of :

A₃ = { w | w such that [w]₃ is divisible by 5. }

From the description 2122 is not in A₃ since [2122]₃ is not divisible by 5 and 202 A₃ since [202]₃ is divisible by 5.

--> Design a DFA that accepts strings in A₃.