## 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.

- ENT, §7.4, Problem 5(a), page 143.
- Let
*n = pq*, where *p* and *q* are distinct
primes. Consider the RSA encryption and decryption functions of
§7.5. Prove that *M*^{kj} is congruent
*M* modulo *n* for **all** residues *M* modulo *n*.
- 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 *b*^{3} is congruent to *a* modulo *p*.
- ENT, §9.3, Problem 1(e), page 200.