Could anyone explain to me why $n$ and $n+1$ share no prime factors. I have found some formal proofs online but unfortunately didn't really understand them.
I accept that it is the case eg: $24 = 2\cdot2\cdot2\cdot3$
$25 = 5\cdot5$
$26 = 2\cdot13$
$27 = 3\cdot3\cdot3$
I found this question in a school text book and it was asking to explain why so I assumed there must be an easy explanation (rather than a formal proof).
Thanks, any help would be greatly appreciated.