I’ll start off by explaining the ‘again’ – I wrote this post, published and tagged, then realised I’d already blogged a while ago about Fermat’s Christmas Theorem and shared some related resources! Version 1 was put together off the back of a UKMT Intermediate Maths Challenge problem – you can read more in the blog post here and get the resources here. I originally wrote this with a group of Year 10s working at (then) grade A/A*, so it’s pitched at about that level.
This Version 2 is much more accessible – all you need is a basic understanding of primes and multiples. I have used this with Year 7 and up, and works well as a ten-minute interesting diversion, either at the beginning or end of a lesson.
At the bottom, I’ve also linked a lengthy but interesting video from Mathologer taking some of these ideas further.
Image credit: Public domain, available https://commons.wikimedia.org/w/index.php?curid=36804
