Question

Prove or disprove that$n^2-79n+1601$ is prime whenever n is a positive integer.

Short answer

$n^2-79n+1601$is disproven.

Step-by-step solution

Step 1

We are going to disprove the statement that $n^2-79n+1601$is a prime whenever n is a positive integer by finding a simple example that shows that this is false.

Step 2

Let $n=1601$. Then:

role="math" localid="1668525242811" $n^2-79n+1601={1601}^2-79\cdot 1601+1601=1601(1601-79+1)=1601\cdot 1523$, and this is obviously a composite number.