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  3. (2) let z/nz be the set of n elements {0, 1, 2, .

(2) Let Z/nZ be the set of n elements {0, 1, 2, . . ....

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Basic Math

(2) Let Z/nZ be the set of n elements {0, 1, 2, . . . , n ? 1}with addition and multiplication modulo n. (a) Which element ofZ/5Z is the additive identity? Which element is the multiplicativeidentity? For each nonzero element of Z/5Z, write out itsmultiplicative inverse. (b) Prove that Z/nZ is a field if and onlyif n is a prime number. [Hint: first work out why it’s not a fieldwhen n isn’t prime. Try some small examples, e.g. n = 4, n =6.]

Answer & Explanation Solved by verified expert
3.8 Ratings (590 Votes)
a The 0 zero element of Z5Z is theadditive identityThe 1 one    See Answer
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