# Base 2014 Termination

**Number Theory**Level 5

Suppose a rational number \(r<1\) can be expressed as \(r=\dfrac{1}{n}\) for some positive integer \(n\). The sum of all possible values of \(r\) such that the base \(2014\) representation of \(r\) is a terminating decimal can be expressed as \(\dfrac{p}{q}\) for coprime positive integers \(p,q\). What is the value of \(p\)?