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    Showing a Residue System Modulo to a Prime Number

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    Suppose that p is a prime number. Show that 0, (p-1)!/2, (p-1)!/3, ..., (p-1)!/(p-1) is a complete residue system modulo p.

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    Definition(Complete residue system) Let . A set of integers
    x1; : : : ; xm is called a complete residue system modulo m, if it contains exactly
    one integer from each equivalence class modulo m. Equivalently, a complete
    residue system modulo m is a set satisfying
    (i) For every there ...

    Solution Summary

    A complete residue system is proven. The solution is detailed and well presented.