Neat little proof

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#213

From: Sol Lerner
Date: Tue, 04 Aug 1992 12:04

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I am trying to remember a neat little proof that sqrt(2) is irrational.  I 
think it went something like this:

Assume sqrt(2) is rational, then sqrt(2) = p/q where q is the LCD.

Then 2 = p squared / q squared
...SOME MAGIC OCCURS...
q can not be the LCD therefore sqrt(2) is irrational.

Can anyone fill in the "...SOME MAGIC OCCURS..." line?

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From: lerner@hilbert.gte.com (Sol Lerner)
Newsgroups: sci.math.num-analysis
Subject: Neat little proof
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Date: 4 Aug 92 12:04:03 GMT
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