Number Theory is one of the cornerstones of math competitions and a vast field explored by professional mathematicians. We are very fortunate to have Dr. Josh Nichols-Barrer present to us next week. Dr. Nichols-Barrer was a very accomplished teenage competitive problem solver who has earned his doctorate at MIT. In addition to Number Theory our students can learn a great deal from his personal experiences. Here is a description of the session in Dr. Nichols-Barrer’s own words:
As you know, each positive integer may be factored uniquely into a product of powers of primes. Do you know why? In this class we will look at the structure of the integers in the simplest terms, and use that for a foundation from which we might actually prove that what we know to be true actually is. In the first half we will recall some things about arithmetic that we know intuitively and can name (with maybe a surprise or two), and in the second half we will proceed to prove (along with some other things which are no less key) unique prime factorization in the integers.