Problem Solving in NT (Day 1 of Week 1)
Just did two problems, and both were hard! So I think one can excuse me for not solving more, but it's true. I did give less time. I am trying to reduce the amount of time I "waste". I did spend ...
INMO
Problem solving in NT (day 2 week 1)
Well, I am finally free! It's more like I was busy with classes and covering up the NT4 course, dang it is hard! Finally got hand of convolutions etc!ISL 2002 N3: Let $p_1,p_2,\ldots,p_n$ be ...
Problem solving in NT ( day 3 Week 1)
OMG Prime number theorem!!! I actually loved it! So today I solved a quite fancy NT problem with other people's help though!Problem: Prove that there exists an interval of the $$ which contains ...
Big ‘O’ notation
Yeyy finally! I got time! I am so happy that I am finally going to read the analytic theory! However, I have added some CS stuff. Not sure if they are accurate. I have taken up CS in school so ...
Problem solving in NT ( day 4 Week 1)
Such a cute problem, although again, swapping the sum is hard.. I should practice more in that area :(Solved with Sidharth and Malay!ProblemProve that$$ \sum_{m=1}^n5^{\omega (m)} \le ...
Problems with meeting people!
Find all positive integers $n < 10^{100}$ for which simultaneously $n$ divides $2^n$, $n-1$ divides $2^n - 1$, and $n-2$ divides $2^n - 2$.Determine all solutions in non-zero integers $a$ and ...
Some Geometry Problems for everyone to try!
These problems are INMO~ish level. So trying this would be a good practice for INMO! Let $ABCD$ be a quadrilateral. Let $M,N,P,Q$ be the midpoints of sides $AB,BC,CD,DA$. Prove that $MNPQ$ ...
IMO Shortlist 2021 C1
I am planning to do at least one ISL every day so that I do not lose my Olympiad touch (and also they are fun to think about!). Today, I tried the 2021 IMO shortlist C1. (2021 ISL C1) Let $S$ ...
IMO Shortlist 2022 C1
Today we shall try IMO Shortlist $2022$ C1. A $\pm 1$-sequence is a sequence of $2022$ numbers $a_1, \ldots, a_{2022},$ each equal to either $+1$ or $-1$. Determine the largest $C$ so ...
EGMO 2024 P2
This problem is the same level as last year's P2 or a bit harder, I feel. No hand diagram because I didn't use any diagram~ (I head solved it) Problem: Let $ABC$ be a triangle ...
Orders and Primitive roots
Orders Given a prime $p$, the order of an integer $a$ modulo $p$, $p\nmid a$, is the smallest positive integer $d$, such that $a^d \equiv 1 \pmod p$. This is denoted $\text{ord}_p(a) = d$. If ...
Some problems in Olympiad Graph theory!
Hello there! It has been a long time since I uploaded a post here. I recently took a class at the European Girls' Mathematical Olympiad Training Camp 2024, held at CMI. Here are a few problems ...
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