Weekly Contest for September 27, 2011
Join the Contest
% cd your-pc2-directory % /homes/cs390cp/pc2/bin/pc2team &
Log in using your individually assigned “teamX” account and password. You can work in the current window/directory, creating a subdirectory for each problem.
Remember: If you've already solved one or more of these problems, try (1) solving again without referring to your old solution, and/or (2) using a different language (Java or C++). If you want to work on an additional problem from the book, let me know.
- A: Find a pattern. The solution is extremely short and efficient.
- B: Repeated divisions is fine (be sure to skip even numbers after 2 and only test as large as necessary).
- C: Observe that, if
n ^ k mod pis
(n ^ (k/2) mod p) ^ 2 mod p. Generalize and handle the case for
- D: Combine the two preludes.
- E: The Extended Euclid Algorithm for GCD (given in the text), given in the text, solves this problem directly.
- F: Brute force factorization is fine. You'll want to keep a table of
(p,e)pairs for each prime,
p, that divides
- G: Theorem: The highest power of
n/p + n/p^2 + n/p^3 …. So,
n!if this sum is at least
- H: The text suggests using the Diophantine solution method given there. Note that you don't actually need to compute the solution, just determine whether or not a solution exists.