Chebyshev sequences degenerating into periodic sequences with realizing finite precision initial value

The short-period problems of Chebyshev sequences had been researched, and aconclusion that Chebyshev sequences of random integer order will degenerateinto short-period sequences while Chebyshev sequence's initial value is afinite decimal had been proved. The equivalent conditions about Chebyshevsequences degenerating into short-period sequences had been shown first, andthen an integer order Chebyshev sequences whose initial value is integermust degenerate into short-period sequence has been proved. Finally, theinitial value conditions has been extended to finite decimal by usingmathematical induction method.