Question

Prove or Disprove:
Given k,n ∈N If k|n! then k|i for some 0 ≤ i ≤ n.

Answer 1

At last a question that I can answer !

Answer 2

Counterexample :
let k = 6, n = 3

Answer 3

6|3!=6 but what is i here?

Answer 4

since n = 3,
i is 0, 1, 2, 3

Answer 5

Hey wait, every integer divides 0, so are you sure the question has no typoes ?

Answer 6

yes it's right

Answer 7

Then the given statement is trivially true
just let \(i=0\)

Answer 8

Every integer divides 0
so every k | 0

Answer 9

maybe proof by induction then

Answer 10

I still feel the question has a typo

Answer 11

no i'm sure is right

Answer 12

\(0\le i \le n\) makes no sense

perhaps it should be \(0\color{red}{\lt} i \le n\) ?