Number Theory

Practice problems, Problem Set, Number Theory, Questions, Answers, Problems, Solutions, Discussions, Walkthroughs, Hints, IOQM, RMO, INMO, Study material, Resources, Olympiad Number Theory Notes, Olympiad Number Theory Problems

Lecture notes on Number Theory (for Math Olympiad — IOQM, RMO, INMO)

Click on the icons below to download.

Number Theory Topics	Links
Induction
Quadratic polynomials
Cubic polynomials
Using identities
Binomial coefficients
Congruences
System of equations
Chinese remainder theorem
Gauss’s lemma
Orders

Lecture notes for Math Olympiad (IOQM, RMO, INMO)

Click on the icons below to download.

Topics	Links
Algebra
Combinatorics
Geometry
INMO Training Camp 2025, MP
IMO Training Camp
MOPSS

These notes

• may be useful
  • to the students who would like to have a look at some of the past RMO problems, in order to have an idea of the notions/topics involved, and/or to have a glimpse before getting started, or just curious about it,
  • to the students, who would like to prepare and would like to have the relevant questions organized across the topics and sub-topics,
• also aim
  • to spread awareness for the Mathematics Olympiad programme in India, conducted by the Homi Bhabha Centre for Science Education (HBCSE), which is the only programme in India leading to participation in the following International Mathematical Olympiads — IMO, APMO, EGMO. No other contests are recognized.
  • to provide resources to the students who may not have access to introductory/preparatory materials related to Mathematics Olympiad.

References/Resources

• Olympiad Training Materials from IMOmath
• Olympiad NT through Challenging Problems, by Justin Stevens, is an introductory olympiad text on number theory.
• Modern Olympiad Number Theory, by Aditya Khurmi, is olympiad-oriented.
• A video by Zlatko Salko Lagumdžija.