Contact Info
Pure MathematicsUniversity of Waterloo
200 University Avenue West
Waterloo, Ontario, Canada
N2L 3G1
Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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Let sq(n) denote the sum of the digits of a number n in base q. For example, s2(n) represents the number of 1s in the binary expansion of n. In 1978, Kenneth B. Stolarsky showed that
lim inf s2(n2) = 0 n→∞ s2(n)
using bounds obtained from analytical methods. In this presentation, we verify the above using algebraic methods to show that we can find an n such that the ratio
s2(n2)
s2 (n) is any given positive rational number. We will also see that a few other intersting results about the
analogous ratio involving other bases and other powers, including fractional exponents.
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Departmental office: MC 5304
Phone: 519 888 4567 x33484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca