An Character of the Period of Modular Sequence of Lucas Sequence

The Modular Sequence of Lucas Sequence is the periodic sequence as well as a simple periodic sequence. According to the definition of modular sequence, we discussed a character of the period of modular sequence of Lucas sequence and obtained a property :If m₁ and m₂ are different positive integers, and the least positive periods of the modular sequenceb_n(m₁)andb_n(m₂)of Lucas sequence L_nare T₁ and T₂ respectively, then the least positive period of the modular sequence b_nm₁, m₂ is T₁, T₂.