# Welcome to GanitCharcha's Publication House

## A Few Interesting Problems on Divisors Counting

We will start this topic with the statement of Fundamental Theorem of Arithmetic.Fundamental Theorem of Arithmetic: Every positive integer $n > 1$ can be...

## Selected Problems on Inequality - Part I

Problem 1: If $a$, $b$ and $c$ are three positivie numbers then, \frac{b^2 + c^2}{b + c} + \frac{c^2 + a^2}{c + a} + \frac{a^2 + b^2}{a + b} \geq a + b +...

## A Note on Factorial and it's Trailing Zeros

DefinitionFor any positive integer $n (>0)$ the factorial of $n$, denoted as $n!$, is defined as\begin{align}n! =...

## Monopole and Electromagnetic duality

In this short note, I explain the magnetic monopole and electromagnetic duality. As we know that mathematics and  physics are intertwined. Here I show...

## Generalization of Divisibility Rules for Primes

For any prime $p$ other than $2$ and $5$ first find out some $x$ such that $px = 10y + 1,$ where $x$ and $y$ are both integers. In number theory, Bezout's...

## Finding routes in a selfish world

In my childhood days, I had to take a long bicycle ride to my school. I had two choices. One way was to take a road which was long yet mostly empty....

## Gold Rush of Our Time - Bitcoin

Bitcoins are digital coins which are not issued by any government, bank, or organization, and rely on cryptographic protocols and a distributed network of...

## A Brief Introduction of Number System

We provide in this note a brief account of our number system. Idea is to introduce different types of numbers and to discuss a few relevant concepts associated...

## A Few Quick Multiplication Tricks

Thousands of numbers can be multiplied by a computer in less than a second, but we human being can not. Easy availability of calculators, computers and smart...