Question

Could some kind person check my proof that gcd(n!, n!+1)=1?

Answer 1

\[n!+1=1\mod1\]\[n!+1=1\mod2\]\[n!+1=1\mod3\]...\[n!+1=1\mod n\]
Therefore \[n!+1\] shares no factors with \[n!\] QED

Answer 2

Remove the first line of the proof, though.

Answer 3

How do you get this?
N!+1 mod 3= 1

Answer 4

N=2
2!+1=3
3 mod 3=0

Answer 5

If N>3, then N! is a multiple of 3, so N!=0mod3

Answer 6

Thus N!+1=1mod3, of course

Answer 7

Then It's fine, your proof seem good

Answer 8

Thanks.