hw3 - a and b are integers and p is prime, then ( a + b ) p...

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Math 465 Problem Set 3 Due Friday, February 8, 2008 1. Prove that if a and b are integers of the form 6 n + 1 or 6 n + 3, then the product ab is also of the form 6 n + 1 or 6 n + 3. 2. Prove that there are infinitely many primes of the form 6 n + 5. 3. Use the binomial theorem to prove that if
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Unformatted text preview: a and b are integers and p is prime, then ( a + b ) p a p + b p (mod p ). 4. Prove that if n > 4 is composite, then ( n-1)! (mod n ) . 5. Solve the following congruences. (a) 91 x 84 (mod 143) (b) 91 x 84 (mod 147) 1...
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