Talk:Integer Combination of Coprime Integers

From ProofWiki
Jump to navigation Jump to search

Proof 1: Bézout's Lemma

Does 'Bézout's Lemma' warrant further justification? I mean, the converse is not true, even though the converse is true for coprime by this --BCLC (talk) 05:12, 4 September 2018 (EDT)

I don't understand the question. BL says: given this gcd you can build this integer combination. No converse needed, as it is not used. --prime mover (talk) 12:22, 31 August 2018 (EDT)
Perhaps for the 'only if' direction, but for the 'if' direction, how do you say that ma+nb=1 implies that gcd(a,b)=1? I don't believe Bézout's Lemma is enough here. However, I think the converse of Bézout's Lemma is used here. While the converse of Bézout's Lemma is not true, it is true for the case that gcd(a,b)=1. --BCLC (talk) 05:12, 4 September 2018 (EDT)
Oh yes, see what you mean. This discussion really needs to go into the appropriate search page for that particular proof. --prime mover (talk) 05:29, 4 September 2018 (EDT)
So, what do I do? --BCLC (talk) 05:46, 4 September 2018 (EDT)
Don't worry about it -- all taken care of. --prime mover (talk) 14:47, 4 September 2018 (EDT)