Category Archives: primes

Fermat’s Little Theorem: proof by modular arithmetic

In a previous post I explained four (mostly) equivalent statements of Fermat’s Little Theorem (which I will abbreviate “FlT”—not “FLT” since that usually refers to Fermat’s Last Theorem, whose proof I am definitely not qualified to write about!). Today I … Continue reading

Posted in number theory, primes, proof | Tagged , , | 7 Comments

Four formats for Fermat: correction!

In my previous post I explained three variants on Fermat’s Little Theorem, as well as a fourth, slightly more general variant, which it turns out is often called Euler’s Totient Theorem. Here’s what I said: If and is any integer, … Continue reading

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Four formats for Fermat

In my previous post I mentioned Fermat’s Little Theorem, a beautiful, fundamental result in number theory that underlies lots of things like public-key cryptography and primality testing. (It’s called “little” to distinguish it from his (in)famous Last Theorem.) There are … Continue reading

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New baby, and primality testing

I have neglected writing on this blog for a while, and here is why: Yes, there is a new small human in my house! So I won’t be writing here regularly for the near future, but do hope to still … Continue reading

Posted in meta, number theory, primes | Tagged , , , | 10 Comments

Games with factorization diagram cards

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)

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!

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