October 2016 – Robert W. Easton

Today’s Lecture: More on Modular Exponentiation and Other Tricks

By Rob|2016-10-25T08:15:38-07:00October 18th, 2016|Categories: Courses, Math 341|

There are a few issues and ideas we didn't get a chance to touch on during today's lecture. Let's take a brief look at some of them here. Modular Exponentiation Today in class we saw an example in which we computed $5^{110}\pmod{131}$ using repeated squaring. However, there was nothing inherently special [...]

Facts About Primes

By Rob|2016-10-10T11:29:30-07:00October 10th, 2016|Categories: Courses, Math 341|Tags: primes|

We saw a lot of different statements about primes today, so much so that you might be feeling a bit overwhelmed. For reference, here is a list of the properties we actually proved: An integer $n>1$ is composite if and only if it has a prime divisor $p\leq \sqrt{n}$. There are infinitely many primes. If $p_1,p_2,p_3,\ldots, [...]