documentation issue

Vincent Lefevre vincent at
Fri Feb 29 12:45:09 CET 2008

On 2008-02-29 10:37:11 +0100, Paul Zimmermann wrote:
> indeed, the fact that the return value is zero for |OP2|=1 does not agree
> with the documentation. Take for example OP1=17 and OP2=1, then ROP=0
> satisfies ROP*OP1 = 1 (mod OP2), thus an inverse exists, and according
> to the documentation, one should get a non-zero return value, with ROP=0
> (this would be the only case where ROP=0).

I wondered whether the notion of inverse existed in the particular case
where 1 = 0, i.e. the ring ({ 0 }, +, *). I searched on MathWorld, and
unfortunately, there's the same mistake:

"The zero element is never invertible, the element 1 is always
invertible and inverse to itself."

which is contradictory in the case 1 = 0.

Vincent Lefèvre <vincent at> - Web: <>
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Work: CR INRIA - computer arithmetic / Arenaire project (LIP, ENS-Lyon)

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