Sunday, 9 February 2014

semigroups - Extend triple of coprime numbers to summation of coprime numbers

I apologize if this has already been answered or is common knowledge. If either of these is the case a reference will suffice.



Given a,b,c positive integers which are pairwise relatively prime, do there exist positive integers x,y,z such that
ax+by=cz and ax,by,cz are pairwise relatively prime?

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