Let Pang g be distinct primes. hetBandn=p8"gel, "show that pa+1_1Lemma 1. Let p = P.p-1 ·be a prime and let a E N. Then v(1) = 1, v(pª) = a + 1, and o(pª)Theorem 2. Suppose that the positive integer n has the prime factorization into distinct primesakn = Pi P2 Pka1...Then(1)v(n) = (a1 +1)(a2 + 1) ·. · (ak +1),ak+1Pkp4 -1 p2+1a1+1pt- 1(2)-o (n) =Pi – 1P2 – 1Pk -1-Lemma 3. Let p>1 be a prime number and let a > 1. Then$(p*) = p* – pª=l = p° (1 - -)a2· Pkaka1Pi P2Theorem 4. Suppose that the positive integer n has the prime factorization n =Thenak$(n) = pª" ( 1 –-)PkP2PiP2Pk= n|1 -P11P21Pk...

Name: Let Pang g be distinct primes. hetBandn=p8"gel, "show that pa+1_1Lemm
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: Let Pang g be distinct primes. hetBandn=p8"gel, "show that pa+1_1Lemma 1. Let p = P.p-1 ·be a prime and let a E N. Then v(1) = 1, v(pª) = a + 1, and o(pª)Theorem 2. Suppose that the positive integer n has the prime factorization into distinct primes