MathDB
Writing 3/n as sum of two reciprocals in exactly 2021 ways

Source: Bundeswettbewerb Mathematik 2021, Round 1 - Problem 2

April 12, 2021
number theorynumber theory proposedreciprocal sum

Problem Statement

The fraction 310\frac{3}{10} can be written as a sum of two reciprocals in exactly two ways: 310=15+110=14+120\frac{3}{10}=\frac{1}{5}+\frac{1}{10}=\frac{1}{4}+\frac{1}{20} a) In how many ways can 32021\frac{3}{2021} be written as a sum of two reciprocals? b) Is there a positive integer nn not divisible by 33 with the property that 3n\frac{3}{n} can be written as a sum of two reciprocals in exactly 20212021 ways?
Back to ProblemsView on AoPS