(b) Prove that if a, b e (Z/nZ)*, then a.be (Z/nZ)*. (Hint: You should start with, "Suppose ā, be (Z/nZ)*. Then there ar

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B Prove That If A B E Z Nz Then A Be Z Nz Hint You Should Start With Suppose A Be Z Nz Then There Ar 1 (22.61 KiB) Viewed 364 times

(b) Prove that if a, b e (Z/nZ)*, then a.be (Z/nZ)*. (Hint: You should start with, "Suppose ā, be (Z/nZ)*. Then there are c, d e (Z/nZ)* such that ca = 1 and db = 1...".] (c) Let a € Z. Show that if (a, n) # 1, then there is some 1 <b<n-1 for which nab. Conclude that if (a, n) + 1, there is some 1 <b<n- 1 for which ā.5 = 7.