Multiplicative inverses in Z/Z[n]

[lime]

Another "warmup" before the test. These are from Dummit's abstract algebra.

For each of the following pairs of integers "a" and "n", show that "a" is relatively prime to "n" and determine multiplicative inverse of "a" in Z/Z[n].

1. a=13; n=20;
2. a=69; n=89;
3. a=1891; n=3797;
4. a=6003722857; n=77695236973.