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.)

Based on trial and error one thing is clear that the only possible solution is if a & b are even and c is odd only then the expression is odd. But no way the total comes to 199.

I've solutions for 299( 12,132,11), 399 (14,252/756,63) but no solutions for 199.

Danish is it true that there is no solution for a,b,c. 

Posted by Salil on 2013-03-25 02:32:25