bq. Given n a prime number and p, q two integer numbers between 0 and n-1 find k such that  p^k^ = q modulo n.
This problem can be solved using the baby step, giant step algorithm which uses the meet in the middle trick.

We can write <tex>k = i\sqrt{n} + j</tex>.

We can write !http://latex.codecogs.com/gif.latex?k%20=%20i[\sqrt{n}%20+%201]%20+%20j!

Notice that i <= sqrt(n) and j <= sqrt(n).
Now our equality looks like this p^ (i ([sqrt(n)] + 1) + j) = q modulo n. We can divide by p^j and get p^(i[sqrt(n)] + 1) = qp^-j modulo n.
Now the application of meet in the middle becomes obvious. We can brute force through the numbers on each side of the equality and find a match.