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Math Help - Chinese Remainder Theorem

  1. #1
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    Chinese Remainder Theorem

    I forgot how to do the Chinese Remainder Theorem which applied for this question:

    Calculate 45^35 modulo 13 given that
    y === 3 mod 13
    and y === 4 mod 45

    Thanks
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  2. #2
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    Quote Originally Posted by knguyen2005 View Post
    y === 3 mod 13
    and y === 4 mod 45
    This is equivalent to, y\equiv 3 + 7\cdot 13(\bmod 13) and y\equiv 4 + 2\cdot 45(\bmod 45).
    Therefore, y\equiv 94(\bmod 13) and y\equiv 94(\bmod 45). Thus, y\equiv 94(\bmod 585).
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