MathDB

ever rational can be written in form of sum of numbers in form a/p^k

Source: 8th QEDMO problem 3 (15. 1. 2011) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 15, 2021

number theoryrational

Problem Statement

Show that every rational number

r

can be written as the sum of numbers in the form

\frac{a}{p^k}

where

p

is prime,

a

is an integer and

k

is natural.