# Number Theory - Discrete Log (Index) - Equation

1. Mar 29, 2007

### mattmns

Here is a silly question from our book, that seems to be a pain to solve:
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Solve the following equation:

$$59^x \equiv 63 \ \text{mod 71}$$
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The idea is to use the discrete log (or index).

Note that 7 is a primitive root mod 71.

The two books I have looked at, solve a problem like this by creating a table with the powers of a primitive root (on the top they have 0, 1, ..., 70 and on the bottom they would have 7^top mod 71). Personally, I don't want to write all that out, so I am curious if there is a way to solve the problem without writing such a table. Any ideas? Thanks!