MathDB

randomly remove 2012 numbers from decimal number 1/p, after the comma

Source: Danube 2012 junior p2

July 22, 2019

number theorydecimal representationdecimalcoprime

Problem Statement

Consider the natural number prime

p, p> 5

. From the decimal number

\frac1p

, randomly remove

2012

numbers, after the comma. Show that the remaining number can be represented as

\frac{a}{b}

, where

a

and

b

are coprime numbers , and

b

is multiple of

p