Express the greatest common divisor of the following pair of integers as a linear
combination of the integers.
117, 213

Question

Express the greatest common divisor of the following pair of integers as a linear 
combination of the integers.
117, 213

anonymous · Answer

Your answer disappeared

anonymous · Answer

Sorry, I misinterpret the problem. We'll have to use the Euclidean algorithm.

anonymous · Answer

Okay 
Let me know what you get please.

anonymous · Answer

see the last example http://www.math.kent.edu/~soprunova/41001f11/notes_9_19.pdf

anonymous · Answer

Okay

anonymous · Answer

still stuck on 213 any help with that one?

anonymous · Answer

oldrin that example was good for 117 but not sure about 213

anonymous · Answer

$$213=117\cdot1+96\117=96\cdot1+21\96=21\cdot4+12\21=12\cdot1+9\12=9\cdot1+3\9=3\cdot3+0$$... so $3$ is our greatest common divisor. Now, we work backwards:$$96=213-117\
21=117-(213-117)=-213+2\cdot117\
12=(213-117)-4(-213+2\cdot117)=5\cdot213-9\cdot117\
9=(-213+2\cdot117)-(5\cdot213-9\cdot117)=-6\cdot213+11\cdot117\
3=(5\cdot213-9\cdot117)-(-6\cdot213+11\cdot117)=11\cdot213-20\cdot117$$

anonymous · Answer

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-spring-2010/lecture-notes/MIT6_042JS10_lec21.pdf There's a useful slide.

anonymous · Answer

Thank you so much