Consider the following statement.

There is an integer *n* such that 

2*n*2 − 5*n* + 2

 is prime.

To prove the statement it suffices to find a value of *n* such that 

(*n*, 2*n*2 − 5*n* + 2)

 satisfies the property 

"2*n*2 − 5*n* + 2

 is prime." Show that you can do this by entering appropriate values for n and 2n^2-5n+2. Enter the solution as a ordered pair.

To show that the statement is true, we need to find an integer \( n \) such that the expression \( 2n^2 - 5n + 2 \) is a prime number. Once we find such an \( n \), we can write the solution as an ordered pair \( (n, 2n^2 - 5n + 2) \).

As shown previously, when \( n = 3 \):

\[
2(3)^2 - 5(3) + 2 = 18 - 15 + 2 = 5
\]

Since 5 is a prime number, the ordered pair that satisfies the statement is:

\[
\boxed{(3, 5)}
\]

This pair demonstrates that there exists an integer \( n = 3 \) such that \( 2n^2 - 5n + 2 \) is prime.

Explore how to find an integer n such that the expression 2n^2 - 5n + 2 results in a prime number. This problem involves the application of the quadratic formula and the prime number theorem to demonstrate the existence of such an integer.

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