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Strange Equation (Posted on 2013-03-11) Difficulty: 3 of 5
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    
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No Solution Comment 10 of 10 |

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
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