Question

prove that if p<= n, then p does not divide n!+1
Please help

Answer 1

this is the proof to the prime numbers being infinite

Answer 2

Is that your question ,

Answer 3

more like...
\[\huge p < n \ \ \rightarrow \ \ \frac{n! + 1}{p}\notin \mathbb{Z}\]

Answer 4

Okay... no need to get so edgy :D\[\huge p \le n \ \ \rightarrow \ \ \frac{n! + 1}{p}\notin \mathbb{Z}\]

Answer 5

p = 1
instant contradiction
http://tinyurl.com/3n3sxpy
haha

Answer 6

1 is not a prime

Answer 7

oh... lol
I didn't know p had to be a prime :)
I just took it for a variable.
My bad :D

Answer 8

Why does p even have to be prime? Doesn't it apply for all integers greater than 1?

Answer 9

yes i understand the question, but i have no idea how to start this question.. D:

Answer 10

Familiar with modular math, @neoc? :)

Answer 11

@terenzreignz yes iam familiar with modular math

Answer 12

That is awesome :)
Then you'd know that if 1 < p < n
then
\[\huge p\lvert n!\]
right?
Because
\[\huge n! = n\cdot(n-1)\cdot...p ...3\cdot2\cdot1\]or something

Answer 13

oh yes! thank you so much! it all make sense now :D

Answer 14

Wow.. that escalated quickly :D
No problem :)