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Tlahuica Numbers

Source: 2022 Mexican Mathematics Olympiad P1

November 8, 2022

primesreciprocals

Problem Statement

A number

x=\frac{1}{p_1}+\frac{1}{p_2}+\dots+\frac{1}{p_k}.

is "Tlahuica" if there exist prime numbers

p_1,\ p_2,\ \dots,\ p_k

such that

x=\frac{1}{p_1}+\frac{1}{p_2}+\dots+\frac{1}{p_k}.

Find the largest Tlahuica number

x

such that

0<x<1

and there exists a positive integer

m\leq 2022

such that

mx

is an integer.

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