Question

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

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$n=41$