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Thread: Split congruence into two pieces

  1. Aug 28th 2009, 07:35 AM #1
    szpengchao
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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. Aug 29th 2009, 03:17 AM #2
    CaptainBlack
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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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