Introduction to Number Theory, NMAI040, fall/winter term 2026/27
I will be teaching this course similarly to the previous years and will follow, more or less,
my lecture notes from 2006.
Exam questions. Exam is oral, with written preparation. Exam questions: TBA.
lecture 1 on October 2, 2026. 1. Diophantine approximations.
Theorems of Dirichlet and Hurwitz on Diophantine approximation. Farey fractions.
lecture 2 on October 9, 2026.
The proof of the theorem of Hurwitz on Diophantine approximation.
Liouville' inequality and the existence of transcendental numbers.
lecture 3 on October 16, 2026.
Hilbert's proof that the number e is transcendental.
lecture 4 on October 23, 2026. 2. Diophantine quations.
Three famous exproblems (Hilbert's 10th problem, FLT, and Catalan's problem).
The CORRECT description of all Pythagoeran triples. Two theorems on Pell equations:
Lagrange's and the description of all solutions in terms of the minimum solution;
beginning of the proof of the former theorem.
lecture 5 on October 30, 2026.
Proofs of the two theorems on Pell equations. ABC conjecture. The Stothers--Mason
theorem (polynomial ABC conjecture); beginning of the proof.
October 2026