If a |b and b |c, then a |c

Name: Problem 1, Chapter 22: A Book of Abstract Algebra
Uploaded: 2021-10-24T01:58:09-08:00
Duration: 2 min 5 s
Channel: Debasish Das
Description: If a |b and b |c, then a |c

step 1 Question number two here we're giving a line like this is the point a this is the point B this i

Question

If $a \mid b$ and $b \mid c$, then $a \mid c$

   If $a \mid b$ and $b \mid c$, then $a \mid c$

A Book of Abstract Algebra

Charles C. Pinter 1982 Edition

Chapter 22, Problem 1

Instant Answer

Solved by Expert Debasish Das

10/24/2021

Step 1

Since $a \mid b$, there exists an integer $k_1$ such that $b = a k_1$. Show more…

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If $a \mid b$ and $b \mid c$, then $a \mid c$

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Key Concepts

Divisibility

Divisibility is a fundamental concept in number theory where one integer divides another if there exists an integer multiplier such that the larger number equals the product of the smaller number and that multiplier. This concept lays the groundwork for understanding factors, multiples, and the structure of integers.

Transitivity of Divisibility

The transitive property in mathematics states that if a relation holds between a first and second element and also holds between the second and a third element, then it holds between the first and third elements. Specifically, in the context of divisibility, if one integer divides a second and that second divides a third, then the first integer divides the third.

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