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jaguarhunter007

  • 2 years ago

Remainder(14! divided by 17) ??

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  1. Yahoo!
    • 2 years ago
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    14! = 14*13*12*11*10*9*8*7*6*5*4*3*2*1

  2. jaguarhunter007
    • 2 years ago
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    help needed folks!!

  3. hartnn
    • 2 years ago
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    maybe wilson theorem might help, check that out.

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

  5. jaguarhunter007
    • 2 years ago
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    wilson theorem shud solve dis..plz elaborate

  6. hartnn
    • 2 years ago
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    (n-1)!+1 = 0 mod n (17-1)!+1 = 0 mod 17 (16)!+1 = 0mod 17 now i m stuck.

  7. jaguarhunter007
    • 2 years ago
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    wot's mod n =??

  8. mathslover
    • 2 years ago
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    well my answer is "very very very long"

  9. mathslover
    • 2 years ago
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    and hopefully wrong .. :P

  10. jaguarhunter007
    • 2 years ago
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    please post it!!! any help wud be appreciated

  11. mathslover
    • 2 years ago
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    Remainder can not be > or equal to 17 and hence my answer is wrong @jaguarhunter007 sorry... :(

  12. mathslover
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=Remainder+when+14%21+%2F+17+

  13. mathslover
    • 2 years ago
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    Wolfram says that as *8* ..

  14. mathslover
    • 2 years ago
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    I think hartnn has a method but thats' too complicated for me now..

  15. hartnn
    • 2 years ago
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    similar problem here: http://math.stackexchange.com/questions/23809/what-is-the-remainder-of-16-is-divided-by-19

  16. oldrin.bataku
    • 2 years ago
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    Just reduce the expression.\[ 16!=16\mod17\\ 240\times14!\mod17=16\mod17\\ 14!=\frac{16}2\mod17\\ \ \ \ \ =8\mod17 \]

  17. jaguarhunter007
    • 2 years ago
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    oldrin where did the 2 come from?? fine till step 2..where did 240 disappear??

  18. oldrin.bataku
    • 2 years ago
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    \[240=2+238=2+17\times14\\240\mod17=2\]

  19. jaguarhunter007
    • 2 years ago
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    wow oldrin thanks!!!

  20. oldrin.bataku
    • 2 years ago
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    @hartnn was on the right track... \[ 16!+1=0\mod17\\ 16!=(-1)\mod17\\ \ \ \ \ \cong16\mod17 \]

  21. jaguarhunter007
    • 2 years ago
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    @oldrin can u give link to properties of mod...how can we move 1 to the left of equation like dat?

  22. oldrin.bataku
    • 2 years ago
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    http://www.math.rutgers.edu/~erowland/modulararithmetic.html

  23. jaguarhunter007
    • 2 years ago
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    oldrin u are the best!

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