Turkish NMO First Round - 1999 P-10 (Number Theory)
Source:
July 3, 2012
greatest common divisor
Problem Statement
For every integers a,b,c whose greatest common divisor is n, if
\begin{array}{l} {x \plus{} 2y \plus{} 3z \equal{} a} \\
{2x \plus{} y \minus{} 2z \equal{} b} \\
{3x \plus{} y \plus{} 5z \equal{} c} \end{array}
has a solution in integers, what is the smallest possible value of positive number n?<spanclass=′latex−bold′>(A)</span>7<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>28<spanclass=′latex−bold′>(D)</span>56<spanclass=′latex−bold′>(E)</span>None