33. gcd(a,b)=1⇒gcd(a^n,b^n )=1| gcd(a,b)=1⇒gcd(a+b,ab)=1 | Problems 2.4 | question 5, 6 and 11 скачать в хорошем качестве

33. gcd(a,b)=1⇒gcd(a^n,b^n )=1| gcd(a,b)=1⇒gcd(a+b,ab)=1 | Problems 2.4 | question 5, 6 and 11

Elementary Number Theory by David M. Burton | Problems 2.4 Chapter#2 Divisibility Theory in the Integers In this lecture I will discuss question number 5, 6 and 11 of problems 2.4. This questions are related to properties of greatest common divisor (gcd). This question can be stated as 1. For n≥1, and positive integers a and b, show that if gcd⁡(a,b)=1, then gcd⁡(a^n,b^n )=1 2. gcd(a,b)=1⇒gcd(a+b,ab)=1 3. gcd(gcd(a,b),c)=gcd(gcd(a,c),b)=gcd(gcd(b,c),a)=d ------------------------------------------------------------------------------------------------------------------------------------------------------- ▶️ Link to 13 Core areas of Number Theory    • Comprehensive Number Theory Course: 13 Cor...   ------------------------------------------------------------------------------------------------------------------------------------------------------- #NumberTheory #DavidMBurton #ElementaryNumberTheory #DivisibilityTheory #GCD #GreatestCommonDivisor #MathematicsLecture #MathsForBSStudents #MathsLectureSeries #HigherMathematics #UniversityMathematics #Maths4U #IntegerProperties #MathTutorial #MathProblemSolving #professorazmatali #academyofmathematicalsciences