I should have said "cannot be bounded by any subexponential function of m and n". Or perhaps I should have said "I had assumed that if you multiply two eventually repeating decimals of period less than or equal to n, you get an eventually repeating decimal whose period is bounded by some polynomial function of n." In fact, my intuition told me that there'd be a quadratic bound. Wrong! Jim On Mon, Sep 29, 2014 at 6:03 PM, Dan Asimov <dasimov@earthlink.net> wrote:
To make a short story long, what does "the period length *can be* exponentially large in n and m" mean?
Maybe it means sup L(rs) over all r, s in Q with L(r) = m, (s) = n, is >= exp(Cm + Dn), where L(t) is the period of the repeating decimal of t in Q, for some C and D in R+. Is that it?
--Dan
On Sep 29, 2014, at 2:53 PM, James Propp <jamespropp@gmail.com> wrote:
I had assumed that if you multiply an eventually repeating decimal of period m and an eventually repeating decimal of period n, you get an eventually repeating decimal whose period is bounded by some polynomial function of m and n. But today I learned from Henry Cohn that that's not true: the period length can be exponentially large in m and n.
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