This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 3

2022 Assara - South Russian Girl's MO, 4
Tags: periodic decimal number , algebra , number theory
Alina knows how to twist a periodic decimal fraction in the following way: she finds the minimum preperiod of the fraction, then takes the number that makes up the period and rearranges the last one in it digit to the beginning of the number. For example, from the fraction, $0.123(56708)$ she will get $0.123(85670)$. What fraction will Alina get from fraction $\frac{503}{2022}$ ?

2005 Spain Mathematical Olympiad, 1
Tags: periodic decimal number , number theory
Prove that for every positive integer $n$, the decimal expression of $\frac{1}{n}+\frac{1}{n+1}+\frac{1}{n+2}$ is periodic .

2023 Romania National Olympiad, 3
Tags: algebra , periodic decimal number
Determine all positive integers $n$ for which the number \[ N = \frac{1}{n \cdot (n + 1)} \] can be represented as a finite decimal fraction.