MathDB

The fraction

\frac{3}{10}

can be written as the sum of two positive fractions with numerator

1

as follows:

\frac{3}{10} =\frac{1}{5}+\frac{1}{10}

and also

\frac{3}{10}=\frac{1}{4}+\frac{1}{20}

. There are the only two ways in which this can be done. In how many ways can

\frac{3}{1984}

be written as the sum of two positive fractions with numerator

1

? Is there a positive integer

n,

not divisible by

3

, such that

\frac{3}{n}

can be written as the sum of two positive fractions with numerator

1

in exactly

1984

ways?

Problem Statement