Remainder

[Acedeal]

If 'p' be a prime, then what is the remainder when (p - 1)! is divided by p?

[-=DoW=- Baseball]

i think it's 0

[Panda]

I'm positive the remainder is p-1. But I sort of divined that answer, so I'm working on coming up with a mathematical proof.

[-=DoW=- SmokieRat]

an odd number

[Panda]

Hehe, I came up with a proof, but I think I'll spare you guys from it.

I had to use a bit of congruences and Wilson's Theorem if any of you are curious because this is essentially a restatement of Wilson's Theorem.. But, yes, the answer is definitely p-1.

If any of you want a hint, though, here's Wilson's Theorem. You should be able to deduce the rest from that.

An integer p>1 is prime if and only if
(p-1)! = -1(mod p)

If you go through the proof of this you'll find that the remainder is p-1.
I was playing around with other possiblities and am finding some very interesting patterns. Probably nothing, but it's all very fun stuff.

[-=DoW=- JBDiamonds]

(p-1) divided by p = -1 answer = -1

[-=DoW=- The Fan]

Wilson’s Theorem states that if p is a prime number, (p – 1)!/p will always leave a remainder of p – 1.

For example, let p be the prime number 5. Then (5 – 1)!/5 = some number with a remainder of 5 – 1.

Doing the math, we get 4!/5 which is 24/5 = 4 with a remainder of 5 – 1, which is 4.

Let’s try the prime number 11. (11- 1)!/11 should give us a remainder of 10.

(11 – 1)!/11 = 10!/11 = 3,628,800/11 = 329890 with a remainder of 10.


That means that JB and Panda are right

[-=DoW=- Deze]

I am very sure the answer is: More beer! :D

[Panda]

Give us more problems like this Ace. They were good stuff. :mrgreen:

[Gandiman]

I failed that corse :) But I like More BEER please :banger:

[-=DoW=- SmokieRat]

If I drank it I'd hafta go with Beer as the answer. But since I don't I'll hafta go with RootBeer then.