Answer
Following the procedure of Example 2, we carry out the Euclidean algorithm to find gcd( 4, 9):
9=2·4+1
4 = 4 · 1
Then we work backwards to rewrite the gcd (the last nonzero remainder, which is 1 here) in terms of 4 and 9:
1=9-2·4
Therefore the Bezout coefficients of 9 and 4 are 1 and -2, respectively. The coefficient of 4 is our desired
answer, namely -2, which is the same as 7 modulo 9. Note that this agrees with our answer in Exercise 3.
Work Step by Step
Following the procedure of Example 2, we carry out the Euclidean algorithm to find gcd( 4, 9):
9=2·4+1
4 = 4 · 1
Then we work backwards to rewrite the gcd (the last nonzero remainder, which is 1 here) in terms of 4 and 9:
1=9-2·4
Therefore the Bezout coefficients of 9 and 4 are 1 and -2, respectively. The coefficient of 4 is our desired
answer, namely -2, which is the same as 7 modulo 9. Note that this agrees with our answer in Exercise 3.
