Tags » Theorem

Fermat’s Little Theorem: proof by necklaces

It’s time for our second proof of Fermat’s Little Theorem, this time using a proof by necklaces. As you know, proof by necklaces is a very standard technique for… wait, what do you mean, you’ve never heard of proof by necklaces?! 896 more words

Number Theory

God is not a Theorem!

I do not understand any other kind of following God than actually engaging a real Divine being through His Spirit. I remember when I was little, nothing was more important to me than truly hearing the voice of God. 181 more words

Faith & Inspiration

Euler’s Theorem: proof by modular arithmetic

In my last post I explained the first proof of Fermat’s Little Theorem: in short, and hence . Today I want to show how to generalize this to prove… 791 more words

Number Theory

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… 648 more words

Number Theory

Wiener's theorem

Wikipedia link.

Let be a locally compact abelian group. Then there exists a Haar measure on and the Fourier transform is defined where is the… 37 more words


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… 186 more words

Number Theory

A characterisation of inner product spaces by Kirk and Smiley

The contents of this post come directly from here.


Let be a normed linear space such that for any vectors the inequality

holds true. 7 more words