Prerequisites:

Students must know the fundamental topics covered in a first semester course in number theory equivalent to MTH 345 (645) as taught at Wake Forest University. Familiarity with divisibility theory and congruences will be expected, as well as experience in devising and writing proofs.

Goals:

The goal of this course will be to improve the problem solving and mathematical writing capabilites of its participants by considering a variety of topics in number theory. A list of probable topics is listed below, but other topics may be considered depending upon interests and time available. Undergraduate credit is obtained by taking this course as MTH 346, and graduate credit by taking this course as MTH 646.

Topics:

• Perfect Numbers, Mersenne Primes, and Fermat Numbers
• Fermat's Last Theorem
• Integers as Sums of Squares
• Fibonacci Numbers and Repunits
• Continued Fractions and Farey Fractions
• Primality Testing and Factorization

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Created 05/31/2001. Last modified 06/01/2001. Email to ekh@wfu.edu