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integers in form 1/a_1+2/a_2+...+9/a_9, where a_i digits

Source: Mexican Mathematical Olympiad 1998 P4

July 28, 2018

number theoryIntegers

Problem Statement

Find all integers that can be written in the form

\frac{1}{a_1}+\frac{2}{a_2}+...+\frac{9}{a_9}

where

a_1,a_2, ...,a_9

are nonzero digits, not necessarily different.