Prove or disprove the following statement: N(n) = n^2 − 81n + 1681 is prime for any positive integer n.

If N has to be composite, it must be a product of two real numbers. N=(n-x)(n-y) x and y must be real. But if you try to find the values of x and y using the formula for quadratic numbers: \(-b \pm \sqrt{b ^{2}-4ac})/2a\] a=1, b=-81, c=1681 You will find x and y to be imaginary. So, this number N can only be expressed as a product of two complex numbers, not real numbers. Hence, the number is prime. Makes sense?

no, your answer is wrong

You mean, the number is not prime?

yes, there are prime numbers generated by this formula, but there also not prime numbers. So prove it :)

Was just browsing through random questions. Came accross. |dw:1334088978935:dw|

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