Let n be an integer, use the definition of even to prove that 18n + 2 is even.18n + 2 =SinceXis an integer,is also an integer.Since 18n +2 equals 2 times an integer, 18n + 2 is even. Let n be an integer, use the definition of odd to prove that 18n + 7 is odd.18n+7= 18SinceX 7is an integer,+1.is also an integer.Since 18n +7 equals 2 times an integer plus one, 18n + 7 is odd.

A number is said to be even if that number is a multiple of 2 and A number is said to be odd if a…

Answered: Let n be an integer, use the definition…

Let n be an integer, use the definition of even to prove that 18n + 2 is even. 18n+2= Since X is an integer, is also an integer. Since 18n + 2 equals 2 times an integer, 18n + 2 is even.

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

Let n be an integer, use the definition of even to prove that 18n + 2 is even.
18n + 2 =
Since
X
is an integer,
is also an integer.
Since 18n +2 equals 2 times an integer, 18n + 2 is even.

Let n be an integer, use the definition of odd to prove that 18n + 7 is odd.
18n+7= 18
Since
X 7
is an integer,
+1.
is also an integer.
Since 18n +7 equals 2 times an integer plus one, 18n + 7 is odd.

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