Talk:Coprime

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Mathematics rating:	Start Class	High Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs references. Geometry guy 22:53, 16 June 2007 (UTC)

Can you add something here about "pairwise coprime" vs. gcd(a,b,c)=1? user:chas_zzz_brown 17:56 7 Oct 02 (UTC)

Contents 1 2 probability 3 The number "0" 4 Properties of Coprimes

[edit]

The definition of Euler's totient function here deviates from the definition in the corresponding article in that the upper inclusive boundary is given as n − 1 instead of n, resulting in a wrong or undefined value for . DirkEn 09:18, 5 September 2006 (UTC)

[edit] probability

The statement about probability of two integers being coprime is fairly misleading at the moment, as nothing has been said about how one chooses two integers "at random". Dmharvey Talk 5 July 2005 18:42 (UTC)

I added some details on the derivation of 6 / π² and what it means to choose two integers "at random." --Dantheox 20:51, 6 May 2006 (UTC)

[edit] The number "0"

Is the number "0" relatively prime with every another integer? —The preceding unsigned comment was added by 89.0.109.36 (talk) 10:02, 30 January 2007 (UTC). I dellete this misconseption

I was about to ask something similar; it's obvious zero is not coprime to any interger other than 1 or -1... but what about those? By definition, they should be coprime, since their greatest factor is 1. Is that right? —Preceding unsigned comment added by 200.199.119.82 (talk) 00:15, August 26, 2007 (UTC)

Right, ±1 is coprime to every integer, including zero. -- EJ 13:46, 8 October 2007 (UTC)

[edit] Properties of Coprimes

I'm very very far from being an expert on the subject, but I notice that the start of the section 'Properties' asserts:

There are a number of conditions which are equivalent to a and b being coprime:

There exist integers x and y such that ax + by = 1 (see Bézout's identity).

Really? 213.70.98.2 15:21, 1 November 2007 (UTC)

Really. Do see Bézout's identity if you want more details. -- EJ 10:53, 2 November 2007 (UTC)