Comment by AnotherGoodName

I wrote an article trying to give a simple overview for teaching. https://rubberduckmaths.com/eulers_theorem

I also added plenty of inline python code blocks students can change and run on the fly.

The reason i wrote this is the hand waving around group theory i saw in other explanations. Namely you shouldn't just say x^y always = x mod m for certain values of y (eg. x^13=x mod 35, even for factors of 35). You should give a detailed, intuitive understanding of why this occurs.