1. If n E Z n>1 . N is prime if and only if (n-2)!= 1 modn

2. Let n be composite and >4. Prove (n-1)! = 0mod n

3. Show that 11 divides 456^654 +123^321

4. Find the solution to 9x=21mod23

Thanks for any help!

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- July 23rd 2008, 08:16 AMkel1487More on Wilson and Fermat
1. If n E Z n>1 . N is prime if and only if (n-2)!= 1 modn

2. Let n be composite and >4. Prove (n-1)! = 0mod n

3. Show that 11 divides 456^654 +123^321

4. Find the solution to 9x=21mod23

Thanks for any help! - July 23rd 2008, 08:42 AMThePerfectHacker
If n is prime then (n-1)!=-1 (n). Write as (n-1)(n-2)!=-1 (n). But n-1=-1 (n). Thus, we are left with after dividing (n-2)!=1 (n).

Quote:

2. Let n be composite and >4. Prove (n-1)! = 0mod n

Quote:

3. Show that 11 divides 456^654 +123^321

Quote:

4. Find the solution to 9x=21mod23

Divide by 3 to get, 3x=7(mod 23) which is equvailent to 3x=30(mod 23).

Thus, we get x=10(mod 23). - July 23rd 2008, 07:07 PMkel1487
Thanks for all of your help!!