MathDB

Unit Fraction Expression

Source: OMM 2007 4

July 19, 2014

number theory unsolvednumber theory

Problem Statement

The fraction

\frac1{10}

can be expressed as the sum of two unit fraction in many ways, for example,

\frac1{30}+\frac1{15}

and

\frac1{60}+\frac1{12}

.
Find the number of ways that

\frac1{2007}

can be expressed as the sum of two distinct positive unit fractions.