Let S = = {u : 1 ≤ u ≤ n − 1 and gcd(n, u) = 1} be the set of units modulo n, where n ≥ 2. Let's denote the elements of

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Let S U 1 U N 1 And Gcd N U 1 Be The Set Of Units Modulo N Where N 2 Let S Denote The Elements Of 1 (20.37 KiB) Viewed 42 times

Let S = = {u : 1 ≤ u ≤ n − 1 and gcd(n, u) = 1} be the set of units modulo n, where n ≥ 2. Let's denote the elements of S by u₁, u2, ···, uk, i.e. S = {u₁, U2, ···, uz}. Prove that (a) U₁+U₂ + ... + Uk = kn and (b) (u₁ U₂ · Uk)² =1 (mod n). - - - Ա