Math Contests
Math Contests
I’m a big fan of math and problem-solving, and math contests have been a huge part of that passion, from competing as a student to now helping out with Indonesia’s IMO team.
Teaching & Achievements
I’ve been involved in math contests for years, first as a competitor and now as a mentor. Here are some of my achievements, listed from most recent:
- Honorable Mention (Top 100), William Lowell Putnam Mathematical Competition 2024
- Top 235 and 312 (7% and 8%), William Lowell Putnam Mathematical Competition 2022 and 2023
- Second Prize, European Mathematical Cup 2020
- Bronze Medal, Tuymaada International Olympiad 2020
- Bronze Medal, Asia Pacific Mathematics Olympiad 2020
- Honorable Mention (IDN 4), Romanian Master of Mathematics 2020
- Absolute Winner, Indonesia National Math Olympiad 2019
- Bronze Medal, Iranian Geometry Olympiad 2018 and 2019
- Bronze Medal, China Southeastern Mathematical Olympiad 2018
I’m part of KTO Matematika, an Indonesian nonprofit math olympiad community run by alumni. I led the group in 2020 and now occasionally propose problems or help with quality checks.
These days, I assist the Indonesian IMO team by teaching, grading, and reviewing problem shortlists. I am also open to teaching, feel free to contact me at viverson@uwaterloo.ca for these type of inquiries.
Handouts
Here are the handouts I used for my sessions in Indonesia IMO 2025 Training Camp:
- (A) Non-Standard Inequalities: View Handout
- (N) Integer Polynomials (Basic): View Handout
- (C) Algorithms: View Handout
- (C) Paths & Cycles: View Handout
Problem Proposals
After retiring from contest math, I have always enjoyed making contest problems alongside my research. Nowadays, I actively propose problems to various national and international math contests. Here are some of my past proposals:
Determine all pairs \((a, b)\) of positive integers for which there exist positive integers \(g\) and \(N\) such that:
\[\gcd(a^n + b, b^n + a) = g\]
holds for all integers \(n \geq N\).
Find the number of positive integer pairs \(1 \leq a, b \leq 2027\) that satisfy:
\[2027 \mid a^6 + b^5 + b^2.\]
Find all functions \(f: \mathbb{N} \to \mathbb{N}\) such that for every prime number \(p\) and natural number \(x\):
\[\{x, f(x), \dots, f^{p-1}(x)\}\]
is a complete residue system modulo \(p\).
Determine all functions \(f: \mathbb{R} \to \mathbb{R}\) such that for every real \(x, y\):
\[f(f(x) + y) = \lfloor x + f(f(y)) \rfloor.\]
Let \(a, b, c\) be three distinct positive integers. Define \(S(a, b, c)\) as the set of all rational roots of \(px^2 + qx + r = 0\) for every permutation \((p, q, r)\) of \((a, b, c)\). For example, \(S(1, 2, 3) = \{-1, -2, -1/2\}\) because the equation \(x^2 + 3x + 2 = 0\) has roots \(-1\) and \(-2\), the equation \(2x^2 + 3x + 1 = 0\) has roots \(-1\) and \(-1/2\), and other permutations yield no rational roots.
Determine the maximum number of elements in \(S(a, b, c)\).
Let \(\mathcal{F}\) be the set of all functions \(f: \mathbb{R} \to \mathbb{R}\) such that:
\[f(x + f(y)) = f(x) + f(y)\]
for every \(x, y \in \mathbb{R}\). Find all rational numbers \(q\) such that for every \(f \in \mathcal{F}\), there exists some \(z \in \mathbb{R}\) satisfying \(f(z) = qz\).
Let \(a, b, c, d\) be real numbers such that \(a^2 + b^2 + c^2 + d^2 = 1\). Determine the minimum value of \((a - b)(b - c)(c - d)(d - a)\) and find all values of \(a, b, c, d\) where this minimum is achieved.