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jaguarhunter007
Remainder(14! divided by 17) ??
14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1
help needed folks!!
maybe wilson theorem might help, check that out.
\[\large{\frac{14*13*12*11*10*9*8*7*6*5*4*3*2*1}{17}}\] Remainder theorem will not work here... at least
wilson theorem shud solve dis..plz elaborate
(n-1)!+1 = 0 mod n (17-1)!+1 = 0 mod 17 (16)!+1 = 0mod 17 now i m stuck.
wot's mod n =??
well my answer is "very very very long"
and hopefully wrong .. :P
please post it!!! any help wud be appreciated
Remainder can not be > or equal to 17 and hence my answer is wrong @jaguarhunter007 sorry... :(
http://www.wolframalpha.com/input/?i=Remainder+when+14%21+%2F+17+
Wolfram says that as *8* ..
I think hartnn has a method but thats' too complicated for me now..
similar problem here: http://math.stackexchange.com/questions/23809/what-is-the-remainder-of-16-is-divided-by-19
Just reduce the expression.\[ 16!=16\mod17\\ 240\times14!\mod17=16\mod17\\ 14!=\frac{16}2\mod17\\ \ \ \ \ =8\mod17 \]
oldrin where did the 2 come from?? fine till step 2..where did 240 disappear??
\[240=2+238=2+17\times14\\240\mod17=2\]
wow oldrin thanks!!!
@hartnn was on the right track... \[ 16!+1=0\mod17\\ 16!=(-1)\mod17\\ \ \ \ \ \cong16\mod17 \]
@oldrin can u give link to properties of mod...how can we move 1 to the left of equation like dat?
http://www.math.rutgers.edu/~erowland/modulararithmetic.html
oldrin u are the best!