Number theory, Spring semester 2026

Books and references:

• We will loosely follow the book Freud-Gyarmati number theory (you can download it in hungarian legally from here).
• For the sum of four squares theorem (and Minkowski's theorem on lattices) i mostly followed this note.
• For the explicit description of the cryptographic algorithms i recommend "The handbook of applied cryptography" by Menezes and Oort (available online, sections 8.1-2 and 8.4) and for Wiener's attack on the RSA this link.
• You can find Euler's proof for the existence of infinitely many primes and that the sum of the reciprocals of primes diverges here (we covered only the first 2 and half pages).
• For the theorems of Erdős-Ginzburg-Ziv and Chevalley-Warning i followed sections 1, 2 and 2.2 of this paper.

Exams:

I started to gather the exam topics here (this will be updated weekly).

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