Re: Learning CRT

In article <1175357197.719698.293270@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
pfntjux@xxxxxxxxx wrote:
Hi All, I'm trying to learn CRT but can't seem to figure out some
things.

First, I try to solve:
x = 1 (mod 2)
x = 1 (mod 3)
x = 1 (mod 4)
x = 1 (mod 5)
x = 1 (mod 6)

These equations are overdetermined. For example, if x = 1 mod 4, you
know immediately that x = 1 mod 2, and if x = 1 mod 6, then you know
immediately that x = 1 mod 2 and x = 1 mod 3. CRT is usually stated
where the moduli are relatively prime. Since knowing x mod 3, mod 4,
and mod 5 tells us x mod 2 and mod 6, we need only solve the middle
three equations. Try that and I bet you will get the answer on the
internet page.

The other comments in this thread pretty clearly explain the errors
in your work, but if you work with relatively prime moduli, you will
easily avoid those errors.

Rob Johnson <rob@xxxxxxxxxxxxxx>
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