If it is not too much trouble, could someone check my multiplicative inverse computation? Here is what I have:

```
gcd( 31, 15 ) = 1 (mod 15) quotient 2
gcd( 1, 0 ) returns gcd of 1
```

Then working backwards:

1 = 31 - 2 * 15 = -30 $\equiv$ 1 (mod 31)

-30 + 31 = 1 therefore the multiplicative inverse of 15 in $Z_{31}$ is 1

This leaves me uneasy, because although I understand the idea, (at least I think I do), I am unsure that I follow the algorithm correctly. The 1 when I am looking for 1 gives me the jibblies.