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On the digits of the multiples of an irrational p-adic number

Published online by Cambridge University Press:  24 October 2008

Kurt Mahler
Kurt Mahler
Affiliation:
Canberra
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Extract

Let α be an irrational p-adic number, r an arbitrary positive integer. Our aim is to prove that there exists a rational integer X satisfying

such that every possible sequence of r digits 0, 1, …, p – 1 occurs infinitely often in the canonical p-adic series for Xα. It is clear that it suffices to prove this result for p-adic integers.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 2 , September 1974 , pp. 417 - 422
Copyright
Copyright © Cambridge Philosophical Society 1974

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