Mathematics OpenStudy (mathmagician):

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

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? OpenStudy (mathmagician): OpenStudy (mani_jha):

You mean, the number is not prime? OpenStudy (mathmagician):

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

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

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