Category Archives: primes

Games with factorization diagram cards

Posted on February 17, 2017 by

Since I published a deck of factorization diagram cards last September, a few teachers have picked up copies of the cards and started using them with their students. I’ve started collecting ideas for games you can play using the cards, … Continue reading →

Posted in arithmetic, counting, games, pattern, pictures, primes, teaching | Tagged , , , , , | 4 Comments

The Möbius function proof, part 2 (the subset parity lemma)

Posted on December 3, 2016 by

Continuing from my previous post, we are in the middle of proving that satisfies the same equation as , that is, and that therefore for all , that is, is the sum of all the th primitive roots of unity. … Continue reading →

Posted in arithmetic, combinatorics, complex numbers, primes, proof | Tagged , , , , , , , , , | 3 Comments

Factorization diagram cards are here!

Posted on September 11, 2016 by

It’s been a long process, but factorization diagram cards are finally available for purchase! If you just want to purchase a set right this minute, then click the above link! If you want to learn more, keep reading. History As … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 2 Comments

Factorization diagram card redesign: feedback welcome!

Posted on August 24, 2016 by

After getting a printed set of factorization diagram cards, I decided there were a few design tweaks I wanted to make. I’ve gone through a few iterations and I think they are definitely better now. Here are some representative samples … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching | Tagged , , | 6 Comments

Factorization diagram cards!

Posted on May 31, 2016 by

I’ve designed a set of factorization diagram cards and had them actually printed. This is one of the first times in my life when I have caused Actual Physical Objects to be created (other than using a printer I guess) … Continue reading →

Posted in arithmetic, counting, pattern, pictures, primes, teaching, video | Tagged , , | 5 Comments

MaBloWriMo 16: Recap and outline

Posted on November 17, 2015 by

We have now established all the facts we will need about groups, and have incidentally just passed the halfway point of MaBloWriMo. This feels like a good time to take a step back and outline what we’ve done so far … Continue reading →

Posted in algebra, arithmetic, computation, famous numbers, group theory, iteration, modular arithmetic, number theory, primes | Tagged , , , , , , , , , | 2 Comments

MaBloWriMo 6: The Proof Begins

Posted on November 7, 2015 by

Today we’re going to start in on proving the Lucas-Lehmer test. Yesterday we saw how, given a Mersenne number , we can define a sequence of integers , with the claim that if and only if is prime. We’re going … Continue reading →

Posted in algebra, arithmetic, computation, number theory, primes | Tagged , , , , , , , | 1 Comment