GCD and Bezout Theorem

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

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

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

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...