question 2: Try to find a positive integer n such that n^2-n+41 is not a prime.

n

^{2}-1 = (n - 1)(n+1)A number n

^{2}-1 will have the factors n-1, n+1.If a number has a factor other than 1 and itself, it is not prime.

In the case of 3. (n=2) n-1 and n+1 are 1 and 3. (1 and itself)

If n - 1 is NOT 1. The factor pair (n-1)(n+1) will NOT be 1 and itself.

Meaning, it will have some other integers as factors.

Hence, if n-1 is NOT 1, n

^{2}-1 is NOT prime.e.g.

n = 5

(n-1) is not 1

n

^{2}-1 has integer factors n-1,n+1...4,6NOT prime

If we only need to find 1 answer for Quest 2. It's fairly simple...

41

^{2}-41+41 = 41^{2}
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