Exercise 1. We proved in the lectures that if p is prime, then Edp (d) = p. (1) Prove that if kEN and p is prime, then Edp (d) = pk. (2) Prove that if p and q are distinct primes, then Ed\pg 4 (d) = pq. (3) Prove that if m, n E N and (m, n) = 1, then (Σ∙()) (Σφ(5) - Σ ×(h). f|n h|mn (4) Prove that if n E N, then Σφ(α) = n. d|n

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