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2013 ToT Fall Junior A p6 3n+1 is a prime number

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March 22, 2020
primeFractiondividesdivisornumber theoryprime numbers

Problem Statement

The number 1−12+13−14+...+12n−1−12n1- \frac12 +\frac13-\frac14+...+\frac{1}{2n-1}-\frac{1}{2n} is represented as an irreducible fraction. If 3n+13n+1 is a prime number, prove that the numerator of this fraction is a multiple of 3n+13n + 1.
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