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Math Help - Prime Related Problem Again

  1. #1
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    Prime Related Problem Again

    let p be an odd prime. Show that the p-3 nubers from 2 to p-2 can be paired up in such a way that the product of each pair is congruent to 1 modulo p and use this to deduce that (p-2)! congruent to 1 mod p.

    I'm having trouble with the first part..
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  2. #2
    Senior Member roninpro's Avatar
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    Try an example. Let p=11. What pairs would you pick from 2, 3, 4, 5, 6, 7, 8, 9\pmod{11}?
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  3. #3
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    3 and 4 ?
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  4. #4
    Senior Member roninpro's Avatar
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    Yes, that works. But the statement says that you can pair up all of those numbers. What are the others?
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