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modular arithmetic watch

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    how come u can cancel multiples if u r using a prime base...but not if u r using a composite one...e.g

    ax=ay (mod p) where p is prime
    then x=y (mod p)

    but u could not do that if p were not prime??? why?
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    also can u say that for example 13=11 (mod 2)??
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    Because if it is prime, and u have
    ab = 0 (mod p)
    Then either a = 0 (mod p), or b = 0 (mod p)

    For composite numbers, it doesnt work like that, for instance

    2*4 = 0 (mod 8)
    but neither 2 or 4 = 0 (mod 8).


    The definition of a prime number is: if p is prime, then
    p|ab implies p|a or p|b.
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    Also, if u have p is composite, then

    ax = ay (mod p)
    x = y (mod p) is only true if a and p are coprime.

    Anyway, ive gotta go, bye.
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    (Original post by JamesF)
    Also, if u have p is composite, then

    ax = ay (mod p)
    x = y (mod p) is only true if a and p are coprime.

    Anyway, ive gotta go, bye.
    so it can be possible if p is not prime as long as p is not a multiple of a?
    is it a definition of modulra arithmetic that p is bigger than a????
 
 
 

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