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On 2012-09-12 12:36 -0700, Andrew Morton wrote:

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The number-theoretical definition of gcd(a, b) on the integers, leaving

aside the case where a and b are both 0, are defined as the greatest

integer which divides both a and b.

An integer x divides y if there exists an integer M such that x*M

equals y.

Observe that all integers divide zero (since we can set M to 0, and

x*0 = 0 for any x). So it's easy to see that the result of gcd(x, 0)

and gcd(0, x) must be |x|.

The case of gcd(0, 0) is tricky. Clearly, as all integers divide zero,

none of these can be the greatest one. So this is normally treated as a

special case, defined to be 0 by convention, as this makes the use of

gcd "nicer" in other areas of mathematics.

Cheers,

--

Nick Bowler, Elliptic Technologies (http://www.elliptictech.com/)

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