So if I have a = qb + r, then the gcd(a,b) = gcd(b,r). Does this formula work for negative r and q and for r>q? Or put another way: what are the restrictions (if any) on this formula?
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I have 3 numbers P,Q and X$\in \mathbb{N}$ and I have that X = P-Q and that gcd(P,Q) = 1. Can I then say that $P=1\cdot Q + X \to gcd(P,Q) = gcd(Q,X) = 1$ ? – Mathaniel Nov 02 '17 at 14:44
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1Answering your question: there are no restrictions as long as $a,b \neq 0$ – davidlowryduda Nov 02 '17 at 14:47