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Math Help - need help

  1. #1
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    need help

    show that 2^45=57 mod 91
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  2. #2
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    Quote Originally Posted by mancillaj3 View Post
    show that 2^45=57 mod 91
    What have you tried so far? If it's the size of the numbers that is putting you off, notice that 91 = 7\times 13. So start by finding 2^45 mod 7 (same problem, but easier arithmetic). Then find 2^45 mod 13.

    Since 57\equiv1\!\!\!\pmod7, you should find that 2^{45}\equiv1\!\!\!\pmod7, and similarly 2^{45}\equiv5\!\!\!\pmod{13}. Conversely (by the Chinese remainder theorem) if x\equiv1\!\!\!\pmod7 and x\equiv5\!\!\!\pmod{13}, then x\equiv57\!\!\!\pmod{91}.
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