Help I'm so confused on how to solve these math problems....

- Find the remainder when 15! is divided by 17
- Find the remainder when 2(26!) is divided by 29
- Verify that 4(29!) + 5! is divisible by 31

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- Mar 28th 2006, 08:21 PMdooz33Remainders
Help I'm so confused on how to solve these math problems....

- Find the remainder when 15! is divided by 17
- Find the remainder when 2(26!) is divided by 29
- Verify that 4(29!) + 5! is divisible by 31

- Mar 29th 2006, 02:28 PMThePerfectHackerQuote:

Originally Posted by**dooz33**

15x14x13x12x11x10x9x8x7x6x5x4x3x2x1

Is the same as,

(-2)x(-3)x(-4)x(-5)x(-6)x(-7)x(-8)x8x7x6x5x4x3x2x1

Thus, you have, (multiply same numbers)

-1x4x9x16x25x36x49x64

Again, since you are working modulo 17 you have,

-1x4x(-8)x(-1)x(-8)x(2)x(-2)x(-4)

Thus, you have, (multiply same numbers)

1x16x64

Thus,

1x(-1)x(-4)

Thus,

4 - Mar 29th 2006, 03:50 PMtopsquark
Now THAT was just too cool! :D

-Dan - Mar 30th 2006, 09:11 PMrgep
I suspect that these are exercises on Wilson's Theorem: $\displaystyle (p-1)! \equiv -1 \pmod p$ for prime $\displaystyle p$.

So for example $\displaystyle 16.15! \equiv -1 \pmod{17}$ gives $\displaystyle 15! \equiv 1$. (ThePerfectHacker dropped some factors from his multiplication.) - Mar 31st 2006, 08:34 AMSkyWatcherQuote:

Originally Posted by**rgep**

wich is the clever according to the questioner supposed knowledge :)

edit: i am on the third's question from here and now!

----- and i know not much (just a little basis on congruence).

edit: for this one i would take PerfectHacker methodologie