My Math Forum  

Go Back   My Math Forum > College Math Forum > Number Theory

Number Theory Number Theory Math Forum

LinkBack Thread Tools Display Modes
September 8th, 2017, 04:31 PM   #1
Joined: Sep 2017
From: San Diego

Posts: 5
Thanks: 0

If a|b and b|a then a=b or a =-b

I'm new to proofs. Is this right.

Prove:If a|b and b|a then a=b or a =-b

Suppose a and b are non-zero integers such that a|b and b|a. Then there must exist integers m and n such that,

a=bm b=an.

Now by substituting b into a=bm we get,


But by dividing both sides by a we get,



m=n=1 or m=n=-1.

If m=n=1 then the a=b, and if m=n=-1 then a=-b. Thus a=b or a=-b, which is what we needed to show.

Thanks for all the comments
Shadow89 is offline  
September 8th, 2017, 06:43 PM   #2
Math Team
Joined: Dec 2013
From: Colombia

Posts: 6,939
Thanks: 2266

Math Focus: Mainly analysis and algebra
I like it.
v8archie is online now  
September 8th, 2017, 06:51 PM   #3
Global Moderator
greg1313's Avatar
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,575
Thanks: 931

Math Focus: Elementary mathematics and beyond
Looks good to me.
greg1313 is offline  

  My Math Forum > College Math Forum > Number Theory

a|b, b|a

Thread Tools
Display Modes

Copyright © 2017 My Math Forum. All rights reserved.