Math CentralQuandaries & Queries


Question from Rimoshika, a student:

determine the greatest common divider (n^2-3n-1,3)

Hi Rimoshika,

You haven't said so but I expect you are to find the greatest common divisor (GCD) of $n^2 - 3n - 1$ and $3$ where $n$ is any positive integer.

The only divisors of $3$ are $1$ and $3$ and hence the GCD is either $1$ or $3.$ Can it be $3?$ Can you find an $n$ so that $3$ is not a divisor of $n^2 - 3n - 1?$


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