29 Sep
2014
29 Sep
'14
4:03 p.m.
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.