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September 8th, 2017, 05:31 PM  #1 
Newbie Joined: Sep 2017 From: San Diego Posts: 7 Thanks: 0  If ab and ba then a=b or a =b
I'm new to proofs. Is this right. Prove:If ab and ba then a=b or a =b Suppose a and b are nonzero integers such that ab and ba. Then there must exist integers m and n such that, a=bm b=an. Now by substituting b into a=bm we get, a=(an)m. But by dividing both sides by a we get, 1=nm. Thus, 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 
September 8th, 2017, 07:43 PM  #2 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,031 Thanks: 2342 Math Focus: Mainly analysis and algebra 
I like it.

September 8th, 2017, 07:51 PM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,641 Thanks: 959 Math Focus: Elementary mathematics and beyond 
Looks good to me.
