# Welcome to GanitCharcha's Publication House

## Mathematics Behind Google Search Engine - A Brief Note

In September $1998$, Google went online and immediately after, it became clear that in comparison to other search engines Google delivered much relevant or...

## A Note on Unit Fractions and its Representations as Sum of Unit Fractions

A rational number or a fraction where the numerator is $1$ and the denominator is any positive integer $n,$ is called a unit fraction and is denoted as...

## 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....