Course

Book 2. Olympiad Number Theory Methods

Book 2. Olympiad Number Theory Methods

  • 1. Advanced GCD Problems
  • 2. Quadratic Residues and Modular Obstructions
  • 3. Multiplicative Order
  • 4. Wilson, Fermat and Euler in Problems
  • 5. p-adic Valuations
  • 6. LTE: Lifting the Exponent
  • 7. Diophantine Equations I: Factorisation and Bounds
  • 8. Diophantine Equations II: Descent and Vieta Jumping
  • 9. Chinese Remainder Theorem and Construction
  • 10. Arithmetic Functions
  • 11. Digits, Bases and Decimal Periods
  • 12. Polynomials, Sequences and Number Theory
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Theory Examples Practice Ladders

Chapters

Chapters

Chapter

Advanced GCD Problems

This module teaches how to turn gcd problems into remainders, linear combinations, prime-divisor conditions, and the Euclidean algorithm on exponents.
20 Problems
Theory Examples Practice

Chapter

Quadratic Residues and Modular Obstructions

This module teaches how to choose a modulus for impossibility proofs, use tables of square residues, and handle prime divisors of sums of squares.
20 Problems
Theory Examples Practice

Chapter

Multiplicative Order

This module teaches power cycles, modular order, restrictions on prime divisors, and Fermat-type numbers.
20 Problems
Theory Examples Practice

Chapter

Wilson, Fermat and Euler in Problems

A practical module on applying Fermat, Euler, and Wilson to powers, inverses, and factorials.
20 Problems
Theory Examples Practice

Chapter

p-adic Valuations

A module on prime exponents in numbers, factorials, binomial coefficients, and maximal divisibility powers.
20 Problems
Theory Examples Practice

Chapter

LTE: Lifting the Exponent

This module introduces LTE as an exact tool for prime exponents in differences of powers and divisibility problems.
20 Problems
Theory Examples Practice

Chapter

Diophantine Equations I: Factorisation and Bounds

This module teaches how to turn first Diophantine problems into a finite search using factorisation, divisibility, and bounds.
20 Problems
Theory Examples Practice

Chapter

Diophantine Equations II: Descent and Vieta Jumping

This module develops infinite descent and Vieta jumping as methods for impossibility, classification, and Markov-type equations.
20 Problems
Theory Examples Practice

Chapter

Chinese Remainder Theorem and Construction

This module teaches CRT for systems of congruences, compatibility, counting solutions, and olympiad constructions.
20 Problems
Theory Examples Practice

Chapter

Arithmetic Functions

This module develops work with \(\tau(n)\), \(\sigma(n)\), \(\varphi(n)\), multiplicativity, and problems about the structure of prime divisors.
20 Problems
Theory Examples Practice

Chapter

Digits, Bases and Decimal Periods

This module translates problems about digits, bases, repunits, and decimal periods into congruences, orders, and the Chinese remainder theorem.
20 Problems
Theory Examples Practice

Chapter

Polynomials, Sequences and Number Theory

This module teaches how to use integer-coefficient polynomials, finite differences, and recurrence periodicity in divisibility problems.
20 Problems
Theory Examples Practice