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September 8th, 2017, 05:31 PM   #1
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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
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September 8th, 2017, 07:43 PM   #2
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I like it.
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September 8th, 2017, 07:51 PM   #3
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Looks good to me.
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