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Chapter 12: Q 28. (page 830)

Show that the statement 鈥�n2-n+41is a prime number鈥� is

true for n=1, but is not true for n=41.

Short Answer

Expert verified

The given statement is shown.

Step by step solution

01

Step 1. Given information

The given statement isn2-n+41.

02

Step 2. 

Let us consider the given statement

n2-n+41is a prime number.

Let us consider the above statement for n=1

12-1+41=41, which is a prime number.

So the given statement is true for n=1.

Let us consider the above statement for n=41

412-41+41=1681, which has a factor 41 apart from the factors 1 and 1681

So the given statement is not true for n=41

As a result, we can say that " n2-n+41is a prime number' is true for n=1, but not true forn=41

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