MathDB
2012 BMT Team 1

Source:

January 5, 2022
number theory

Problem Statement

Let SS be the set of all rational numbers x∈[0,1]x \in [0, 1] with repeating base 66 expansion x=0.a1a2...ak‾=0.a1a2...aka1a2...ak...x = 0.\overline{a_1a_2 ... a_k} = 0.a_1a_2...a_ka_1a_2...a_k... for some finite sequence {ai}i=1k\{a_i\}^{k}_{i=1} of distinct nonnegative integers less than 66. What is the sum of all numbers that can be written in this form? (Put your answer in base 1010.)
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