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## GCD and Bezout Theorem

Get motivated Consider the equation 2019x + 2020y = 2018. Are there integers x and y that satisfy this equation? Concepts in this lesson will help you to answer this question and more. Concept – GCD, Bezout Theorem GCD of two numbers a and b is their greatest...

## Cyclic Groups in TIFR Entrance

Concept – Cyclic Groups Let’s discuss the concept of Cyclic Groups. A cyclic group G is a group that can be generated by a single element. In particular, if $G = \{ a, b, c, d, .. \}$, $*$ is the group operation and $a$ is a generating element, then...

## Division Algorithm

Concept – Division Algorithm Let’s discuss the concept of Division Algorithm. Given any integers a and b with 𝑎≠0 there exist unique integers q and r such that 𝑏=𝑞𝑎+𝑟,𝑜≤𝑟<|𝑎| . If a does not divide b then r satisfies the stronger inequality...

## Gauss Trick in ISI Entrance

Problem – Gauss Trick (ISI Entrance) Let’s learn Gauss Trick for ISI Entrance. If k is an odd positive integer, prove that for any integer $\mathbf{ n \ge 1 , 1^k + 2^k + \cdots + n^k }$ is divisible by $\mathbf{ \frac {n(n+1)}{2} }$ Key Concepts Gauss...

## Bijection Principle from I.S.I. Entrance

Try the problem This problem of Bijection Principle is from B.Stat, B.Math Entrance. How many natural numbers less that $10^8$ are there, whose sum of digits equals 7? Watch the first hint Other useful links:-...