Welcome to our community

Be a part of something great, join today!

[SOLVED] Composite number

  • Thread starter
  • Admin
  • #1

anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,756
Prove that the number $9999999+1999000$ is composite.
 

kaliprasad

Well-known member
Mar 31, 2013
1,322
Let x = 1000 to keep it simple
So we get
$9999999+1999000 = 10^7-1 + 1999 * 1000$
$= 10 * 10^ 6 - 1+ (2000-1)* 1000$
$= 10 x^2 - 1 + (2x-1) x$ putting 1000 = x
$=12x^2 - x - 1$
$= (4x+1)(3x-1)$
$= 4001 * 2999$ putting back x = 1000

Hence it is composite
 
Last edited: