Explore BrainMass

Explore BrainMass

    Binomial Expansion in a Ring

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:05 pm ad1c9bdddf
    https://brainmass.com/math/ring-theory/binomial-expansion-ring-28714

    Solution Summary

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

    $2.19

    ADVERTISEMENT