Unformatted text preview: a)7,11 b) 101,303 c) 1331, 5005 d) 5040, 7700. 3. Show that √ 2 + √ 3 is irrational, by ﬁnding a monic polynomial of which it is the root. 4. Prove that there are inﬁnitely many primes of the form 6 k + 5, where k is a positive integer. 5. Using the Fermat factorization method, factor each of the following positive integers: 73, 8051, 46009, 3200399. 6. Factoring kn by the Fermat factorization method, where k is a small positive integer, is sometimes easier than factoring n by this method. For example, show it is easier to factor 2703 than to factor 901. 1...
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 Fall '07
 Santos
 Number Theory, Complex Numbers, Natural number, Prime number

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