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    Binomial Expansion in a Ring

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    Let p be a prime. Show that in the ring Z-p (set of integers modulo p) we have (a+b)^p = a^p+b^p for all a, b in Z-p. The following hint was given: observe that the usual binomial expansion for (a+b)^n is valid in a commutative ring.

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    Solution Summary

    Binomial expansion in a ring is investigated. The solution is detailed and well presented.