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CTK Exchange
Otto Murphy
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Mar-17-10, 08:42 PM (EST) |
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"proving the Chinese remainder theorem for more than 2 eqns"
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The proof provided on this website only proves the Chinese remainder theorem for two simultaneous equations. How can this be used to prove the theorem for more than two equations? Is there some kind of inductive argument? |
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Otto Murphy
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Mar-19-10, 11:08 PM (EST) |
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4. "RE: proving the Chinese remainder theorem for more than 2"
In response to message #2
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Don't you have to show that: s = n_k+1 (mod gcd(lcm(m1, m2, ..., mk), m_k+1)) is true before you can find n: n = s (mod lcm(m_1, m_2, ..., m_k))
n = n_k+1 (mod m_k+1) I can't figure out how to prove that the first eqn. is true. |
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You may be curious to have a look at the old CTK Exchange archive.
Please do not post there.
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