## jaguarhunter007 3 years ago Remainder(14! divided by 17) ??

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1. Yahoo!

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

2. jaguarhunter007

help needed folks!!

3. hartnn

maybe wilson theorem might help, check that out.

4. mathslover

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

5. jaguarhunter007

wilson theorem shud solve dis..plz elaborate

6. hartnn

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

7. jaguarhunter007

wot's mod n =??

8. mathslover

well my answer is "very very very long"

9. mathslover

and hopefully wrong .. :P

10. jaguarhunter007

please post it!!! any help wud be appreciated

11. mathslover

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

12. mathslover
13. mathslover

Wolfram says that as *8* ..

14. mathslover

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

15. hartnn
16. oldrin.bataku

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

17. jaguarhunter007

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

18. oldrin.bataku

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

19. jaguarhunter007

wow oldrin thanks!!!

20. oldrin.bataku

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

21. jaguarhunter007

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

22. oldrin.bataku
23. jaguarhunter007

oldrin u are the best!