MA-410 Homework 4

Due at the beginning of class, Monday, April 25, 2005

Solutions may be submitted in person in class, or you may email an ASCII text, html, or postscipt/pdf-formatted document to me.
Note my office hours on my schedule.

  1. ENT, §7.4, Problem 5(a), page 143.
  2. Let n = pq, where p and q are distinct primes. Consider the RSA encryption and decryption functions of §7.5. Prove that Mkj is congruent M modulo n for all residues M modulo n.
  3. Let p be an odd prime such that 3 does not divide p-1. Prove that for any residue a modulo p there exists a residue b modulo p such that b3 is congruent to a modulo p.
  4. ENT, §9.3, Problem 1(e), page 200.