Chapter 12: Q 28. (page 830)

Show that the statement “ $n^{2} - n + 41$ is a prime number” 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

Step 1. Given information

The given statement is $n^{2} - n + 41$ .

Step 2.

Let us consider the given statement

$n^{2} - n + 41$ is a prime number.

Let us consider the above statement for $n = 1$

$1^{2} - 1 + 41 = 41$ , which is a prime number.

So the given statement is true for $n = 1$ .

Let us consider the above statement for $n = 41$

$41^{2} - 41 + 41 = 1681$ , 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 " $n^{2} - n + 41$ is a prime number' is true for $n = 1$ , but not true for $n = 41$

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Show that the statement “ $n^{2} - n + 41$ is a prime number” is
true for $n = 1$ , but is not true for $n = 41$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2.

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Show that the statement “n2-n+41is a prime number” istrue for n=1, but is not true for n=41.

Short Answer

Step by step solution

Step 1. Given information

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Statistics

Decision Maths

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Show that the statement “ $n^{2} - n + 41$ is a prime number” is
true for $n = 1$ , but is not true for $n = 41$ .