Reprint: An unsolved problem on the powers of (1968)

  • Kurt Mahler


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

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