Show that the number $9999999+1999000$ is composite.
Problem
Source: Ukraine 1999 Grade 9 P3
Tags: number theory
jasperE3
10.05.2021 16:20
It's $2999\cdot4001$ after some manipulations.
judgefan99
10.05.2021 17:41
After manipulation we get 2999*4001. This is the prime factorization of the number. Therefore, because it has two prime factors, it is by definition composite.
ilovepizza2020
10.05.2021 17:46
jasperE3 wrote: It's $2999\cdot4001$ after some manipulations. Work? How did you get 2999 or 4001 as a factor?
jasperE3
10.05.2021 17:59
$1999000+9999999=12\cdot10^6-10^3-1=(3000-1)(4000+1)=2999\cdot4001$