[IEEE 2016 IEEE 10th International Conference on Application of Information and Communication Technologies (AICT) - Baku, Azerbaijan (2016.10.12-2016.10.14)] 2016 IEEE 10th International Conference on Application of Information and Communication Technologies (AICT) - Existence of repetitions of digits in the construction of periodic sequences related to 3x+1 problem: Proof of the theorem on the periods in the 3-adic representation of terms of periodic sequences that appear in Collatz problem