Unformatted text preview: allowed to be a prime number? 4. Find the ±rst positive integer value of n such that the formula n 2 + n +29 does not result in a prime number. 5. Consider an integer c with prime factorization c = p i 1 1 p i 2 2 · · · p i k k , with p 1 , . . . p k distinct. Show that in the prime factorization of c n , all the exponents are divisible by n . 6. Use the last execise to show that if an n-th power is the product of two relatively prime factors: c n = ab, ( a, b ) = 1 then each of the factors is itself an n-th power. 1...
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- Fall '08
- Prime number, prime Factorization, Mersenne prime, relatively prime factors