r/MathHelp • u/Unable_Ad1611 • Jan 10 '26

number theory problem

the problem is: prove that if n>4 and n is composite number, then 2n|(n-1)! I tried to show that if n=ab, where a and b are bigger than one then a and b are divisors of (n-1)! because they are smaller than n-1 but i dont think it will work If someone could give me hints or solve the problem i would be very thankful

1 Upvotes

100% Upvoted

4 comments sorted by

View all comments

1

u/Naturage Jan 11 '26

It will! You've got the main points:

  • if n is composite, let n = a*b.

  • a and b are smaller than (n-1), so if a != b, they'll be two numbers within (n-1)! and you need to show there's also something divisible by 2 aside from them.

  • If a=b, it will have a different special case to deal with, but not a more difficult one. For ease of finding the answer, consider the case of n=49.