Question

(2) For an integer n, let Z/nZ denote the set of equivalence classes [k) tez: k -é is divisible by n (a) Prove that the set Z/nZ has n elements. (b) Find a minimal set of representatives for these n elements. (c) Prove that the operation gives a well-defined addition on Z/nZ Hint: The operution should not depend on the choice of coset representatives Verify that this gives Z/n2 the structure of an ahelian group. Be sure to verify all of t properties for an abelian group (e) Write an explicit rule for computing the sum using the representatives found in part (b) Hint: Use a piecewise function

Answer 1

sez : k-λ :s divisible by n then L and hence a dich on CO p and g to cloiu Let ihe any inte ger B diviienalovitfm t be any enteaes

n elements'

on Z 7几e unde 2 仏

elen te rince (I n m-l To Phow