Math Problem Statement
Consider the following statement.
There is an integer n such that
2n2 − 5n + 2
is prime.
To prove the statement it suffices to find a value of n such that
(n, 2n2 − 5n + 2)
satisfies the property
"2n2 − 5n + 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.
Solution
To show that the statement is true, we need to find an integer such that the expression is a prime number. Once we find such an , we can write the solution as an ordered pair .
As shown previously, when :
Since 5 is a prime number, the ordered pair that satisfies the statement is:
This pair demonstrates that there exists an integer such that is prime.
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Math Problem Analysis
Mathematical Concepts
Prime numbers
Quadratic equations
Formulas
Quadratic formula
Theorems
Prime number theorem
Suitable Grade Level
Grades 10-12