Unformatted text preview: →∞ n k +1 σ ( n k ) , where σ denotes, as usual, the function whose value at m is the sum of the divisors of m . 5. Show that there are an inﬁnite number of primes which are congruent to 7 mod 8. [If P 1 ,. .. ,P n are such primes, consider ( P 1 ··· P n ) 2-2.] 6. Let n be a positive integer. Show that 2 n ≡ 1 mod n if and only if n = 1. [For n > 1, consider the situation modulo the smallest prime number dividing n .]...
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This note was uploaded on 10/31/2009 for the course STAT 131A taught by Professor Isber during the Spring '08 term at Berkeley.
- Spring '08