MathDB
Digits of numbers

Source:

April 28, 2022

Problem Statement

Determine the sum of all positive integers n<100n<100 satisfying the following expression. ∑k=0⌊log⁡10n⌋110k(n  ( mod   10k+1)−n  ( mod   10k))=∏k=0⌊log⁡10n⌋110k(n  ( mod   10k+1)−n  ( mod   10k)).\sum_{k=0}^{\lfloor{\log_{10} n}\rfloor}\frac{1}{10^k}\left(n \; (\bmod \;{10^{k+1})}-n \;(\bmod \;{10^k)}\right)=\prod_{k=0}^{\lfloor{\log_{10} n}\rfloor}\frac{1}{10^k}\left(n \; (\bmod\; 10^{k+1})-n \;(\bmod\; 10^k)\right). Here, ∑\textstyle\sum and ∏\textstyle\prod represent sum and product, respectively.
2022 CCA Math Bonanza Lightning Round 3.3
Back to ProblemsView on AoPS