The following problem was posed in the March 2025 issue of Crux Mathematicorum. OC 722 : Let $p$ and $q$ be distinct primes. Assume that the four numbers $p^{23}, p^{24}, q^{23}, q^{24}$ occur (not necessarily consecutively) in a decreasing arithmetic progression. Show that the primes $p$ and $q$ themselves also appear in that same progression. Solution by […]
The following problem was posed in the March 2025 issue of Crux Mathematicorum. Solution to MA311 by Srikanth, Mudhitha Maths Academy, Chennai. Authors: Srikanth is the instructor at Mudhitha Maths Academy, Chennai. He is very fond of problem solving and puzzle games. He is an assistant professor of mathematics by the week, enjoys designing software
The following problem was posed in the March 2025 issue of Crux Mathematicorum. Solution to MA312 by Srikanth and Achudhan: Authors: R.Achudhan is a 9th grader who is enrolled in Target RMO 25 at Mudhitha Maths Academy ,Chennai. He loves solving problems especially non-routine kind. His love for mathematics and problem solving has kindled his
The following problem was posed in the March 2025 issue of Crux Mathematicorum. Solution to MA311 by Srikanth and Achudhan. Authors: R.Achudhan is a 9th grader who is enrolled in Target RMO 25 at Mudhitha Maths Academy ,Chennai. He loves solving problems especially non-routine kind. His love for mathematics and problem solving has kindled his
Here’s an interesting problem related to voting and ballot counts:
Suppose A and B win p and q votes respectively in an election with p > q. While counting the ballots, what is the probability that A always remains ahead of B throughout the count?
Andre’s reflection trick solves this problem.
In this post, we will define binomial coefficients using integration of complex valued functions and prove high school identities using integration methods. 12th standard students who are learning calculus should be able to follow this post. You can consider this as a practice in integration theory. I usually call such fun extras as JEE side
Introduction A polynomial in one variable $x$ with real coefficients is an expression that can be made by adding, multiplying, subtracting real numbers and the variable $x$. For instance, consider the expression $x^2 + 3x +2$, which is simply the wordy algorithm Think of a number, square it and add it to three times to
“One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work.” –Matthew Pordage In this blog post, we discuss the definition and properties of inversion, suggest a few configurations, outline the solution to a sample problem, and conclude with a few exercises. Inversion: A recap
In this post we focus on inequalities. First we look at tips from Engel’s book, then we solve a couple of problems using these tips. Finally I leave you with an exercise set.
Usually olympiad algebra problems involves solving equations, proving inequalities and playing with polynomials. So I have collected a few basic problems. To keep you on your toes, I claim one proof is incomplete. Which one?
