Remainder(14! divided by 17) ??

Question

anonymous · Answer

14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1

anonymous · Answer

help needed folks!!

hartnn · Answer

maybe wilson theorem might help, check that out.

mathslover · Answer

$$\large{\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{17}}$$
Remainder theorem will not work here... at least

anonymous · Answer

wilson theorem shud solve dis..plz elaborate

hartnn · Answer

(n-1)!+1 = 0 mod n
(17-1)!+1 = 0 mod 17
(16)!+1 = 0mod 17
now i m stuck.

anonymous · Answer

wot's mod n =??

mathslover · Answer

well my answer is "very very very long"

mathslover · Answer

and hopefully wrong .. :P

anonymous · Answer

please post it!!!
any help wud be appreciated

mathslover · Answer

Remainder can not be > or equal to 17 and hence my answer is wrong @jaguarhunter007 
sorry... :(

mathslover · Answer

mathslover · Answer

Wolfram says that as *8* ..

mathslover · Answer

I think hartnn has a method but thats' too complicated for me now..

hartnn · Answer

anonymous · Answer

Just reduce the expression.$$
16!=16\mod17\
240\times14!\mod17=16\mod17\
14!=\frac{16}2\mod17\
\ \ \ \ =8\mod17
$$

anonymous · Answer

oldrin where did the 2 come from?? fine till step 2..where did 240 disappear??

anonymous · Answer

$$240=2+238=2+17\times14\240\mod17=2$$

anonymous · Answer

wow oldrin thanks!!!

anonymous · Answer

@hartnn was on the right track... $$
16!+1=0\mod17\
16!=(-1)\mod17\
\ \ \ \ \cong16\mod17
$$

anonymous · Answer

@oldrin can u give link to properties of mod...how can we move 1 to the left of equation like dat?

anonymous · Answer

anonymous · Answer

oldrin u are the best!