Maths Olympiad Daily Problems

For any positive integer a, σ(a) denotes the sum of the positive integer divisors of a. Let n be the least positive integer such that σ(a^n) – 1 is divisible by 2021 for all positive integers a. If the sum of the prime factors in the prime factorization of n is M, then find M/5

Hello, guys, the mock has officially ended. The results will be sent via email by Thursday. Only 13 responses, I guess people have yet to finish the syllabus. So the next mock will again be on Sunday(14/06/2026). The next one will be subject-based on algebra. 30 algebra questions of the IOQM pattern. Be ready and sharpen your algebra skills.

Guys, how will you prove that (4^n)-3n-1 is always divisible by 9 for n belongs to positive integer?

Beautiful question

Sup everyone am making a mock IOQM paper too, don't worry I don't know the answer of any and am gonna attempt it along with ya guys lol. Looking at the pace, expect the paper to be sent across by the next week or so.

Last few problems from Utkarsh badmosh 🔪🔪🔪

A clearer picture of the question

Everyone is advised to give this mock. Don't underestimate it, given that you are a serious IOQM aspirant. A mate pf ours, probably younger than most of us here, made this paper for us so that we can give our best, leave alone cracking it. Don't you think you should attempt it for the sake of his time and respect? It's disheartening to see you people ignoring it like this. What even is tye meaning of 5.3k subscribers when even 10 of u can't give a well made doable mock. Please, don't downplay it like this.