Question

Solve: 91x  = 189 mod 231

Answer 1

first find the inverse of 91 mod 231 using the euclidean algorithm

Answer 2

scratch that, 91 and 231 are not relatively prime, they are both divisible by 7

Answer 3

so divide everything by 7 and start with
\[13x\equiv 27(\text { mod }33)\]

Answer 4

we can find the inverse of 13 using the euclidean algorithm

Answer 5

\[33-2\times 13+7\]
\[13=7+6\]
\[7=6+1\] work backwards to solve for 1

Answer 6

first line should be
\[33=2\times13+7\]

Answer 7

work backwards and get
\[1=7-6\]
\[1=7-(13-7)=2\times 7-13\]
\[1=2(33-2\times 13)-13=2\times 33-5\times 13\]

Answer 8

so the "bezou coefficients" are 2 and -5, therefore -5 is the inverse of 13 mod 33

gotta run, hope you can finish from there
answer is 30

Answer 9

cook a bunch for me!!!