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I know all 8 idempotents in $\Bbb Z_{2024}$ are: $1265, 760, 1288, 737, 1496, 529, 0, 1$. I hope this helps somehow. Please help me, this question failed me in the exam (((

Robert Shore
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Sindi Hall
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    Did you cover the Chinese Remainder Theorem? – GEdgar Feb 26 '24 at 18:48
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    @arthur Not if you consider the isomorphism as an isomorphism of rings. Given ring theory is tagged, and not group theory, it seems implied, if not specified in the question. – Thomas Andrews Feb 26 '24 at 19:13
  • In group theory, $$ is used to denote the free product. For the direct product, use \times to get $\times$. In Ring theory, $$ is not a good symbol either. – Arturo Magidin Feb 26 '24 at 19:22
  • You need only the idempotents $,1265 \to (1,0,0),\ 1288\to (0,1,0),,1496\to (0,0,1),$ to apply the common CRT formula in the linked dupe. – Bill Dubuque Feb 26 '24 at 19:34
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    @ThomasAndrews You're right, and the mention of idempotents should have tipped me off as well. – Arthur Feb 26 '24 at 19:40

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