# A problem by Kwesi Levy

Level pending

Let $$p$$ be any positive prime number. What is the length of the longest repetend* required to express $$0.1_{10}$$ in base-$$p$$?

*The "repetend" is the repeating block of a non-terminating, rational decimal. For example, in base-10, $$\frac{1}{3} = 0.\overline{3}$$ has a repetend of length 1 while $$\frac{1}{990} = 0.0\overline{01}$$ has a repetend of length 2 (we ignore the leading decimal[s]).

×