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Math Help - Split congruence into two pieces

  1. #1
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    Split congruence into two pieces

     a^{N-1}=1 \ mod \ N

    if we now N is composite, how can u split this into two congruences which are equivalent to original one?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by szpengchao View Post
     a^{N-1}=1 \ mod \ N

    if we now N is composite, how can u split this into two congruences which are equivalent to original one?
    If N=AB, then:

    a^N = a^A a^{B-1}\equiv 1 \ \text{mod} \ N = [a^A \text{ mod } N][a^{B-1} \text{ mod } N] \text{ mod } N

    CB
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