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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.
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