Teaching materials · Cycle 4
Advanced Number Theory.
Three live sessions on the tools that carry olympiad number theory beyond the elementary, Fermat, Euler, multiplicative orders, the Lifting the Exponent lemma, and primitive roots, closed with a participant teacher presentation.
Coach: Dr. Dušan Djukić (University of Belgrade · Mathematical Institute SANU). Three live sessions, 24 April, 9 May, 24 May 2026. Closed on 14 June 2026 with a participant teacher presentation on selected Cycle 4 exercises.
What the cycle covered
- 24 April 2026. Fermat's Little Theorem, Euler's Theorem, multiplicative orders, exponential Diophantine equations.
- 9 May 2026. Lifting the Exponent lemma and p adic valuation.
- 24 May 2026. Primitive roots and residues.
- 14 June 2026, participant teacher presentation. Cohort members presented worked solutions to selected problems from Cycle 4.
The cycle followed the arc needed for serious competition teaching: from the two theorems every olympiad student meets, through orders and LTE as the first serious lemmas that separate hard problems from routine ones, to primitive roots as an organising idea for residue arithmetic.
Exercise collection
The problems from Cycle IV.
The full exercise collection worked across this cycle, kept as a single document so the mathematics can be revisited in its original form.
These are the exercises used in the cycle's sessions. Individual problems are drawn from the olympiad problem literature and compiled for the Academy's teaching. External publications are listed on the Resources page.