Beautiful and elegantly written! 
(I should do more of that; my work is messy and sloppy)
Welcome to the Community btw!
Thanks, I’m trying to write all of them up into a document and I saw someone posted this site so I thought I may as well upload the work cause I was doing it anyway.
(I sat this paper on monday lol)
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Also for anyone reading the solution, I freely use both modular arithmetic and divisibility notation. It’s well worth learning both for STEP as in the number theory questions you can save a lot of time
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Fantastic content!!