[seqfan] Re: An arithmetic conjecture

Rainer Rosenthal r.rosenthal at web.de
Mon Mar 16 17:20:56 CET 2009

David Wilson wrote:
> DW> To my knowledge, no one knows how to prove your statement.
> DW> Without getting heavily into it, this problem belongs to a class
> of problems
> DW> with problems like:
> DW> Does every sufficiently large power of 2 include the digit 0 in base 10?

I'd like to ask my preferred book UPINT, but I am not sure
where I could find an answer (or at least related questions).
The actual problem, posed by Peter Luschny, was: what can
be said about the remainders of floor(2^m/3^k) modulo 6?
His problem restated:

    ================= Conjecture ===================
    For all m > 26 there exists some k > 0 such that
             floor(2^m / 3^k) = 3 (mod 6).

Could someone please be so kind as to give me a pointer
to UPINT (Unsolved Problems in Number Theory)? I have
the third edition available at home.

Best regards,

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