author was so excited to point at calculus, that he forgot to derive actual mod3000 answer from chinese remainders...
and it seems much more intuitive for me to see this technique as "find x mod p^n, then apply x->ans+p*x transformation and do everything at mod p^n+1" - and to derive that it results in derivatives from that
In some sense the title is a bit misleading (one is led to think of Analytic Number Theory). I'd rather use the title "Using differentials to...", which is more precise, as there is not exactly any "calculus" going on but there is indeed differential algebra and differential "number theory", so to speak.
Analytic number theory exists and involves calculus, but it's not what the linked post is about. The article talks about Hensel's lemma, which is a purely algebraic statement with a purely algebraic proof, which, however, is inspired by techniques from calculus. This is typically still categorized as algebraic number theory.
and it seems much more intuitive for me to see this technique as "find x mod p^n, then apply x->ans+p*x transformation and do everything at mod p^n+1" - and to derive that it results in derivatives from that
But great and elegant article. Thanks.
https://en.wikipedia.org/wiki/Analytic_number_theory
The prime number theorem, on how prime numbers are distributed amongst the integers, was first proved using analytic techniques.