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In a 100-digit n, the decimal period length of 1/n > 2011

Source: XVIII Tuymaada Mathematical Olympiad (2011), Junior Level

July 29, 2011
Eulerquadraticsnumber theory unsolvednumber theory

Problem Statement

Prove that, among 100000100000 consecutive 100100-digit positive integers, there is an integer nn such that the length of the period of the decimal expansion of 1n\frac1n is greater than 20112011.
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