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How to determine all the faithful irreducible representations of $\mathbb Z_n$ and $D_{2n}$ over $GF(p)$, where $p$ is a prime not dividing $n$?

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    See also http://mathoverflow.net/questions/102573/structure-of-f-pg-for-finite-group-g http://math.stackexchange.com/questions/172534/for-which-values-of-n-is-the-polynomial-px-1xx2-cdotsxn-irreducible/172540#comment396429_172540 http://math.stackexchange.com/questions/172468/for-what-n-k-there-exists-a-polynomial-px-in-f-2x-s-t-degp-k-and2012-07-22
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    http://math.stackexchange.com/questions/153429/irreducible-representations-of-a-cyclic-group-over-a-field-of-prime-order2012-07-22
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    http://math.stackexchange.com/questions/167979/representation-of-cyclic-group-over-finite-field?lq=12012-07-24

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