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Unformatted text preview: . If p is a prime, show that all prime divisors of 2 p-1 are congruent to 1 mod p . (For example, 2 11-1 = 23 89 is divisible by the primes 23 and 89 and by no others.) 5 (7 points) . Let be the Mobius function, and let be the function whose value on n 1 is the number of divisors of n . Explain why the function F ( n ) := X d | n ( d ) ( d ) satises the relation F ( n 1 n 2 ) = F ( n 1 ) F ( n 2 ) when gcd( n 1 , n 2 ) = 1. Calculate F ( p e ) when p is a prime and e is a positive integer....
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- Spring '08