 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Strange Equation (Posted on 2013-03-11) 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.)

 No Solution Yet Submitted by Danish Ahmed Khan No Rating Comments: ( Back to comment list | You must be logged in to post comments.) re: solution | Comment 2 of 10 | (In reply to solution by xdog)

your error is in assuming (m,np)=(m,n)*(m,p)
A quick counter example is
m=2, n=4, p=8
(m,n)=(m,p)=2
(m,n)*(m,p)=4
however, (m,np)=2

I had a similar though as you of somehow simplifying the equation to be strictly in terms of (a,b), (a,c), and (b,c).  However, this boils down to finding (m,np) in terms of (m,n), (m,p), and (n,p).  Unfortunately I have not been able to find an equation that works in all cases.

 Posted by Daniel on 2013-03-15 02:02:43 Please log in:
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