Is the following statement true or false? For every integer n, if n is prime then (-1)^= -1. Which of the choices below answers the question? (Select all that apply.) The statement is true. For instance, when n = 3, (-1) = (-1)³ = -1. The statement is true because all prime numbers are odd, and -1 raised to any odd power is -1. The statement is false because when n = 0, (-1) = (-1)⁰ = 1. The statement is false because not every prime number is odd, and -1 raised to an even power is 1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question

Help

Is the following statement true or false?
For every integer n, if n is prime then (-1)" = -1.
Which of the choices below answers the question? (Select all that apply.)
V The statement is true. For instance, when n = 3, (-1)" - (-1)3 = -1.
The statement is true because all prime numbers are odd, and -1 raised to any odd power is -1.
The statement is false because when n = 0, (-1)" = (-1)° = 1.
O The statement is false because not every prime number is odd, and -1 raised to an even power is 1.
Transcribed Image Text:Is the following statement true or false? For every integer n, if n is prime then (-1)" = -1. Which of the choices below answers the question? (Select all that apply.) V The statement is true. For instance, when n = 3, (-1)" - (-1)3 = -1. The statement is true because all prime numbers are odd, and -1 raised to any odd power is -1. The statement is false because when n = 0, (-1)" = (-1)° = 1. O The statement is false because not every prime number is odd, and -1 raised to an even power is 1.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,