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 September 8th, 2017, 04:31 PM #1 Newbie   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, 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, 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.
 September 8th, 2017, 06:51 PM #3 Global Moderator     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.

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