First, the 3x+1 problem is transformed into the decision of the terms valued 1 of the all-odd 3x+1 sequences. Then, the property of the all-odd 3x+1 sequences is used to obtain the equations with equal terms and the sufficient and necessary conditions for the all-odd 3x+1 sequences to have equal terms. Then, the uniqueness of the characteristic solutions of the equations with equal terms is proved. At last, based on the above results the 3x+1 problem is proved to be true.

Xunwei Zhou received Bachelor of Engineering and postgraduate diploma in Beijing University of Technology. He is a professor emeritus in Beining Union University. He constructs mutually-inversistic logic and applies it to computer science and artificial intelligence. He published about 80 refereed papers and authored 4 monographs on them. He is a senior member of Chinese Computer Federation, a supervisor of Beijing Logical Association.