Can Every Positive Integer Sequence Contain Only Composite Numbers?

[NightFire]

Hey everyone I am new in this forum, and it looks great ! :)
i have this problem to prove this question.id really appreciate our help for this one:

Prove that for every positive integer n,there are n consecutive composite integers.
there's a the hint in the question that says; consider the n consecutive integers starting with (n+1)! + 2

thanks
for ur help
Roy

 

[HallsofIvy]

Okay, (n+1)!+ 2 is composite because it is divisible by 2. (do you see why?)

(n+1)!+ 3 is composite because it is divisible by 3.

(n+1)!+ 4 is composite because it is divisible by 4.

etc.

 

[NightFire]

Okay, (n+1)!+ 2 is composite because it is divisible by 2. (do you see why?)

(n+1)!+ 3 is composite because it is divisible by 3.

(n+1)!+ 4 is composite because it is divisible by 4.

etc.

i don't see why it is divisible by 2, would you like to explain it please?
much appreciated

 

[JThompson]

Are you familiar with the factorial?
k!=k*(k-1)*(k-2)*...*3*2*1

Do you now see why it is divisible by 2?

 

[moonman239]

This thread doesn't belong in this forum.

Is this a homework question? If so, this really should be in the "Homework/Coursework Questions" forum.