what is the GCD of n and n+1

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- Nov 6th 2009, 08:10 PMlebanonwaht is ?
what is the GCD of n and n+1

- Nov 6th 2009, 08:12 PMBacteriusReply
It is $\displaystyle 1$, obviously ... can $\displaystyle n + 1$ possibly divide $\displaystyle n$ ? No. You can investigate this fraction :

$\displaystyle \frac{\ n + 1}{n}$

And saying that two consecutive numbers have a common factor (except 1) is saying that :

$\displaystyle (n + 1) mod n = 0$

Which is impossible.