Tag Archives: gcd

2021 AMC 10B Problem 5

Posted on November 30, 2022 by Sumant Sumant
Posted in Algebra | Tagged , , | Leave a comment

Why GCD*LCM=Product of numbers themselves

Posted on November 19, 2022 by Sumant Sumant
Posted in Abstract Algebra, Number Theory | Tagged , | Leave a comment

If (a,b)=1 and c divides a+b, prove that (a,c)=(b,c)=1

Posted on November 30, 2020 by Sumant Sumant

Prove that if If and divides , prove that Let’s first understand this with an example. and this means and indeed this is true. A lemma and Proof: As also . Therefore Thus Given Let’s assume that means and . … Continue reading →

Posted in Number Theory, Proof | Tagged , | 1 Comment

Euclid’s Algorithm Proof

Posted on November 6, 2019 by Sumant Sumant
Posted in Abstract Algebra, Combinatorics, Number Theory, Proof | Tagged | Leave a comment

Two Important Results in Number Theory

Posted on November 6, 2019 by Sumant Sumant
Posted in Number Theory, Proof | Tagged | Leave a comment

Binomial Identity

Posted on May 22, 2014 by Sumant Sumant

What is the gcd of There are few things one should notice: 1. gcd will also divide each individual term 2. gcd will also divide the sum of all the terms since it divides each individual term 3. sum of … Continue reading →

Posted in Algebra, Number Theory, Prime Numbers, Sequences, Series | Tagged , , , | Leave a comment