Solve the equation
(a^2,b^2)+(a,bc)+(b,ac)+(c,ab)=199. in positive integers.
(Here (x,y) denotes the greatest common divisor of x and y.)

(In reply to re: solution by Daniel)

Yes, bad assumption on my part, although I think maybe it's true if (m,n)=1.  Another thought:  given (a,b)=d then a=dx and b=dy, so maybe what's needed is to deal with x,y instead of a,b.  Or somehow the equation ax+by=d comes in.  I'll give it another go with your correction in mind.  Thanks. 

Posted by xdog on 2013-03-15 11:53:51