Reprint: An unsolved problem on the powers of 3/23/2 (1968)

  • Kurt Mahler


One says that α>0\alpha>0 is a ZZ-number if 0\le {\alpha (3/2)^n\}<1/2, where {x\} denotes the fractional part of xx. In this paper, while not showing existence, Mahler proves that the set of ZZ-numbers is at most countable. More specifically, Mahler shows that, up to xx, there are at most x0.7Zx^{0.7} Z-numbers.

Reprint of the author's paper [J. Aust. Math. Soc. 8, 313--321 (1968; Zbl 0155.09501)].