#### CSCI 3104 - Algorithms - Fall 2010

### Problem Set #2

#### Due: 12pm, Jan 26th, 2011

1. Suppose you wanted to determine if a decimal number is divisible by 99.
Give a quick method for doing this. (Hint: convert the number to base-100
by grouping pairs of digits together, then use the same approach we used
for testing for divisibility by 3.) Justify your answer.
2. Text problem 1.12. Use only paper. Show your work.

3. Text problem 1.13. Use only paper. Show your work.

4. One of the largest natural integer constants we know of is
`M=808017424794512875886459904961710757005754368000000000`. This is
the size of an object of mathematics that is just there (humans didn't
invent it).

Just for fun, compute M^{M} mod 2011. Use a computer for this one;
include source code with your solution.

5. Text problem 1.18. Show your work.