Calculate politeness of a number online, i.e., the number of ways it can be expressed as the sum of consecutive integers.

Online tool for prime factorization and calculating sum of proper divisors. The algorithm is implemented in JavaScript and UI in Vue.js.

Online tool that helps you do prime factorization. The algorithm is implemented in JavaScript and UI in Vue.js.

Hard to believe that I don't remember seeing Descartes' rules of signs before -- you'd think this is impossible given the time I spent on ...

This is the last of a small series of similar and basic results in convex geometry.

Previous I used Caratheodory's theorem to prove Radon's theorem, now I'm going to prove the former.

I came across Radon's theorem the other day, and found this proof. It must have been discovered before.

There are 2n+1 coins each associated with a weight. When we remove any coin, we can split the rest into two piles each with n coins...

Given a sequence of (n) integers (a_1,ldots,a_n), we map it to ...

On the 2D plane there are (n) blue and (n) red points, no three of them are co-linear. Then we can always pair a blue point with a red ...

It is said to be well-known, but perhaps I've never seen it before:

Let (A(n)) denote the number of sequences (a_1ge a_2gecdots{}ge a_k) of positive integers for which (a_1+cdots+a_k = n) and each ...

We call a (5)-tuple of integers arrangeable if its elements can be labeled (a, b, c, d, e) in some order so that (a-b+c-d+e=29). Deter...

I found a different solution to the second part of this problem. We define a chessboard polygon to be a polygon whose edges are situate...

Let (m_1, m_2, ldots, m_n) be a collection of (n) positive integers, not necessarily distinct. For any sequence of integers (A = (a_1...

The problem is rephrased. Q: A diamond of size n consists of 2n rows of nodes with lengths from top to bottom being 1, 3, 5, ..., 2n-1...

Let (P_1, P_2, dots, P_{2n}) be (2n) distinct points on the unit circle (x^2+y^2=1), other than ((1,0)). Each point is colored eit...

In a mathematical competition some competitors are friends. Friendship is always mutual. Call a group of competitors a clique if each two of...

There are n>=2 line segments in the plane such that every two segments cross and no three segments meet at a point. Geoff has to choose an ...

International Mathematical Olympiad (IMO) 2014 Problem 6

Asian Pacific Mathematics Olympiad (APMO) 2015 Problem 4

International Mathematical Olympiad (IMO) 2010 Problem 6

International Mathematical Olympiad (IMO) 2015 Problem 6

United States of America Mathematical Olympiad (USAMO) 2015 Problem 3

The infamous Grasshopper problem

Evaluate Multivariate Normal Distribution with NumPy in Python.