Question

determine the gcd of 6123 and 2913 and write it as a linear combination

Answer 1

\[6123 =2\cdot 2913 +297\]\[2913=9\cdot 297+240\]\[297=1\cdot 240 +57\]\[240=4\cdot57+12\]\[57=4\cdot12+9\]\[12=9\cdot 1+3\]\[9=3\cdot3+0\]So the gcd of 6123 and 2913 is 3. To write it as a linear combination, rewrite each of the above equations to solve for the remainder, and then perform a bunch of substitutions starting with \(3=12-1\cdot9\).

Answer 2

I'll let you do that part, but I can check your answer when I get back on.