Prove:Let a, b, and c be integers. IfSuppose a, b, c are integers with (a(a - b) | c, then a | c.b) | c. Then c =(a b) for some integer k, so c =]a, ·so a c.

Answered: Image /qna-images/answer/325ce5e9-ec1a-4fa9-87a8-1499e71bc13a.jpg

Answered: Prove: Let a, b, and c be integers. If…

Prove: Let a, b, and c be integers. If (a - b) | c, then a | c. Suppose a, b, c are integers with (a - b) | c. Then c = | (a b) for some integer k, so c = a, so a c.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter2: Basic Linear Algebra

Section: Chapter Questions

Problem 15RP

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Concept explainers

Problems on numbers

Number theory is one of the most appealing topics in mathematics. Given one or more numeric values, a numeric algorithm performs some computation. The use of number theory in computing is important for applications like in the case of cryptographic algorithms. Number theory is also used in various applications such as calculating hash functions or in information security. Euclid’s algorithm is one of the oldest number-theoretic algorithms which is used to calculate the greatest common divisor of two numbers.

Question

Prove:
Let a, b, and c be integers. If
Suppose a, b, c are integers with (a
(a - b) | c, then a | c.
b) | c. Then c =
(a b) for some integer k, so c =
]a, ·
so a c.

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