1
$\begingroup$

If $n$ is a natural number, then what are the possible values(s) of gcd $(n+1, 2-n)$?

There are six options: $1,2,3,4,5,6$

I think the answer is $1$

$\endgroup$
  • 2
    $\begingroup$ Consider $n=2$. $\endgroup$ – Brian M. Scott Dec 11 '13 at 21:08
  • 1
    $\begingroup$ They are asking what the possible options are, meaning that you are choosing which of those $6$ values is possible. There will be multiple answers. $\endgroup$ – Cameron Buie Dec 11 '13 at 21:08
5
$\begingroup$

$gcd(a,b)=gcd(a,a+b)$

$gcd (n+1,2−n)=gcd(n+1,3)\in\{1,3\}$

$\endgroup$
2
$\begingroup$

If $p|n+1$ and $p|2-n$, then $p|n+1+2-n=3$, thus $p=1$ or $p=3$.

The case $p=3$ can happen with $n=2+3k$.

For other value of $n$, the gcd is of course 1.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.