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

Question

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

mani_jha · Answer

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?

mathmagician · Answer

no, your answer is wrong

mani_jha · Answer

You mean, the number is not prime?

mathmagician · Answer

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

anonymous · Answer

Was just browsing through random questions.
Came accross.
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