Number Theory

The student will verify some fundamental properties of natural numbers, express numbers in different bases, find the greatest common divisors of two numbers by Euclid's algorithm, factor an integer by various methods such as Fermat's and Euler's methods, and become acquainted with several solved and unsolved problems in number theory. The student will find the number of divisors of a natural number, the sum of the divisors, the product of the divisors, and the means of the divisors; become acquainted with perfect, multiple perfect, amicable and sociable numbers; analyze various theorems related to perfect numbers; study Euler's function; solve simple diophantine equations; and study congruences.

Fall, Spring

011279