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Unformatted text preview: norm of , denoted N ( ), as N ( ) = a 2 + 5 b 2 . (a) Show that if = a + b 5 and = c + d 5, where a,b,c,d Z , then N ( ) = N ( ) N ( ). (b) Show that the numbers 1 + 5 and 15 are prime numbers, that is, there are no numbers = a + b 5 and = c + d 5 dierent from 1 such that 1 5 = . (Hint: Use part (a)). (c) Find two dierent factorizations of the number 21 into primes of the form a + b 5, where a and b are integers. 4. Rosen 3.5 #45, pg. 119 Show that 2 + 3 is irrational. 1...
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 Spring '10
 anne
 Number Theory, Integers

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