Figured it would be a quick review of ideas that turned into a nightmare...(adsbygoogle = window.adsbygoogle || []).push({});

[tex] x \equiv i ([/tex]mod [tex]1 + i)[/tex]

[tex] x \equiv 1 ([/tex]mod [tex]2-i)[/tex]

[tex] x \equiv 1+i ([/tex]mod [tex]3+4i)[/tex]

we find [tex]s \equiv 0 [/tex](mod [tex]1+i)[/tex] and [tex]s \equiv 1 [/tex](mod [tex]5+10i)[/tex] but this is easy.

So now find [tex]s' \equiv 0 [/tex](mod [tex]2-i)[/tex] and [tex]s' \equiv 1 [/tex](mod [tex]-1+7i)[/tex] is complicated...Using the euclidean algorithm I got that there is a gcd of [tex]\pm i[/tex] for [tex]2-i[/tex] and [tex]-1+7i[/tex]

I think i'm kind of stuck, I also can't seem to find

[tex]s'' \equiv 0 [/tex](mod [tex]3+4i)[/tex] and [tex]s'' \equiv 1 [/tex](mod [tex]3+i)[/tex].

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# Chinese remainder theorem (Gaussian ints)

Can you offer guidance or do you also need help?

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