0
$\begingroup$

Prove that if $a \in \mathbb Z$ then the only positive divisor of both $a$ and $a + 1$ is $1$.

When I saw this statement I didn't understand it. The only way that I can see it being true is if a is a negative number but since a ∈ Z a could also be positive and thus it could have more than one positive divisor. If that's the case would I have to disprove this instead of proving? And what would be the best way to do that?

$\endgroup$
  • 1
    $\begingroup$ What common divisors do 2 and 3 have? Or 3 and 4 or 9 and 10? $\endgroup$ – Paul Sundheim Sep 22 '14 at 0:18
  • $\begingroup$ I think it's asking for a single number that divides both $a$ and $a+1$. $\endgroup$ – Trurl Sep 22 '14 at 0:19
  • $\begingroup$ Please choose descriptive titles. The original title, Prove or Disprove??? carried virtually no information of what the problem is about. $\endgroup$ – user147263 Sep 22 '14 at 1:11
0
$\begingroup$

You seem to have misunderstood the question. As far as I can tell you are thinking about divisors of $a$ and $a+1$ separately, but the question is asking you to show that the only positive number which is a divisor of both $a$ and $a+1$ simultaneously is $1$.

This statement is true and a hint for the proof is: any number which is a divisor of two integers (simultaneously) is also a divisor of their difference.

$\endgroup$
0
$\begingroup$

If $n$ divides both $a$ and $a+1$, it would also divide $a+1-a$.

$\endgroup$

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.