A brief guide to Number Theory

1Authors

About the Authors.

CO-AUTHOR

Aritra Saha

I am Aritra Saha from Malda, West Bengal. I am a math enthusiast currently in grade 12 as of 2026. I started preparing for math Olympiads back in grade 7. From the very beginning, Number Theory was the one topic I was most excited to study and solve problems in (definitely not because I was bad at the other topics!).

I wrote my first INMO in 2023 and was devastated in 2025 after missing the cutoff by just 4 points. However, my love for Number Theory kept me motivated, and I decided to write something on the subject, which led to the initial spark that made us write the book.

During this same period, I became deeply involved in the wider math community. I joined the Sophie Fellowship for the 2025 Cohort and soon after became a part of the Online Math Club (OMC) organizing team. I began teaching classes there — which you can find on the OMC YouTube Channel — and took part in creating problem sets and selecting problems for team contests. During this time, we were both constantly working on the book, specifically at night.

I qualified through IOQM and RMO for the 2025–26 Olympiad cycle. Between all my preparation for JEE, Olympiad, and OMC duties, eventually the day of INMO 2026 came. A fun fact about this journey: the day before the INMO, just to calm my nerves, I was actually writing out the proof for Zsigmondy's Theorem (though the book ultimately features a different proof than the one I drafted that day). If you have seen the 2026 INMO paper, you know the rest. Thanks to that topic, I cleared the exam and proudly became an INMO Awardee.

I have been incredibly fortunate to participate in several mathematical programs that have deeply shaped my understanding of the subject over the last few years. These experiences have taught me as much about perseverance as they have about mathematics:

Along with attending the IMOTC in 2026, I had the opportunity to participate in STEMS (2026) and the Enumeration Camp in both 2025 and 2026, where I was happy to place second in the 2026 finals.
I was honoured to be selected for the Maths Beyond Limits camp in the Balkans (though I was ultimately unable to attend) and enjoyed participating in the Sharygin Geometry Olympiad, advancing to Round 2 for grade 10.
I recently advanced past Round 1 of the SRMC and am currently preparing for the Round 2 examination this October.

When I am not doing math, I have a variety of other interests. I enjoy solving Rubik's Cubes, though I wouldn't call myself a speed-solver. I also spend time solving variant Sudokus. I am an avid chess player (Chess.com username: AritraSaha13) and recently competed in my first offline tournament at ISI, Kolkata. Furthermore, I spend a lot of time playing GeoGuessr, enjoy watching competitive Scrabble, and occasionally look back fondly on my days of active quizzing, where I represented my school and district at the state level.

One of my absolute favorite mathematical hobbies is proposing original problems. You will actually find two or three of my own problems featured in this book. I also proposed Problem 2 and Problem 6 for the LMAO Revenge Contest, which you can check out on the IMOTC 2026 page on AoPS.

If anyone wants to reach out to me personally, you can connect via AoPS, where my username is CrystalMind (though I am not very active there), or via Discord, where my username is aritra2008.

CO-AUTHOR

Riddhiman Seal

I am Riddhiman Seal, a Grade 12 student and math enthusiast based in Mumbai. My journey into mathematics began in elementary school, but my passion for competitive problem-solving truly ignited in Grade 8 when my cousin introduced me to Olympiads. Tackling IOQM-level problems for the first time was a steep challenge, but it opened up a refreshing side of mathematics that I quickly grew to love. My first IOQM was in 2022. I found the paper very hard, but when I saw the solutions after coming back home, it gave me lots of “aha” moments. Despite spectacularly failing the paper, I kept working on Olympiads in search of more such “aha” moments. Within Olympiad math, I focus heavily on geometry and number theory.

Over the years, I have participated in the Indian Olympiad cycle (IOQM, RMO, INMO) alongside individual contests like the AMC and AIME. Some key highlights include securing the highest score in the Mumbai region in RMO 2024 and 2025, placing 1st in the subjective round at the MTRP camp at ISI Kolkata as well as 6th overall, and earning a 3rd Diploma in the Sharygin Geometry Olympiad. Together with my co-author Aritra, I have also competed in team events — placing 2nd in the Power Round at the Berkeley Math Tournament and 1st overall in the Oxford Mathematics Team Competition. Outside of competing, I am a staff member at the Online Math Club, where I deliver lectures, curate problem sets, draft mock papers, and assist with club administration. I am also part of the Sophie Fellowship, an initiative providing resources and a community for math Olympiad students.

My favourite problems are probably Mexico National Olympiad 2020/3 for combinatorics (realizing that the answer is not odds but actually the primes took me so long!), IMO 2019/6 for geometry (the synthetic solution is very challenging), and Iran TST 2014/9 for number theory (an amazing mix of combinatorial and analytic number theory). I also enjoy exploring configurations in geometry by simply opening GeoGebra, marking random centres and points, and seeing what follows.

Beyond mathematics, I am a Dan 2 black belt in Taekwondo with ten years of training, and enjoyed teaching students in lower belts. I even competed in tournaments like DSO and CICSE, where I won multiple medals. My other big interest is football. Due to time constraints in recent years, I have been unable to follow it thoroughly, but I do tune in to watch big matches, Champions League knockouts, and of course, the FIFA World Cup. I have also represented my club, Sumit's Football Association, in the Youth Premier League.

In lower grades, I also tried out other sports like swimming and chess. I could not continue swimming beyond grade 5 due to the lockdown. I took classes for chess, and even represented my school in a few tournaments. Some of my other interests include reading (my favourite series is for sure Percy Jackson and The Heroes of Olympus) and playing the piano (I have taken classes, but unfortunately haven't given any of the Trinity grade exams). During the lockdown, I also created 3 YouTube channels: one about the Rubik's Cube (Rubik's Brothers), one about Lego animations (Animator ZRB), and one about the piano (Illuminotes).

If anyone wants to get in touch with me, you can reach out via AoPS, where my username is simplisticformulas, or via Discord, where my username is simplisticformulas.

2The Story

The Story Behind the Book.

The inspiration for this book came from a gap the two noticed while studying Olympiad number theory: while standard classic texts exist, many modern, recurring ideas are scattered across short handouts without a centralized place to practice. The idea for writing something together was born on 24th April 2025 when Aritra messaged Riddhiman saying:

Message from Aritra: Bro, I was thinking of writing a NT handout from May. Do you wanna collaborate and share your thoughts?

On 7th May, they joined their first Google Meet and started working on the first chapter. By the beginning of June, they had already written about 30 pages, and by the end of July, 80 pages were written. Their pace slowed down a bit in the next two months. From December to February, the writing came to an almost complete halt due to preparations for INMO, JEE, and some applications. They started writing again in March, and by the middle of May, all but the last chapter was done. Around this time, they also started revising and editing the previous chapters, as well as getting in touch with publishers. At long last, on the 20th of June, they finished the more-or-less final version of the draft.

The process had so many ups and downs, but despite the challenges, they persevered and managed to create the resource they wished they had when they started their Olympiad journey.