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# h4 115A - equations a 2 x 3 y 4 z = 5 b 7 x 21 y 35 z = 8 c...

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MAT 115A University of California Fall 2010 Homework 4 due October 27, 2010 1. Rosen 3.6 #4 (a)-(c), pg. 131 Using the Fermat factorization method, factor each of the following positive integers: 8051, 73, 46009. 2. Rosen 3.6 #20, pg. 132 Find all primes of the form 2 2 n + 5, where n is a nonnegative integer. 3. Rosen 3.6 #24, pg. 133 Factoring kn by the Fermat factorization method, where k is a small integer, is sometimes easier than factoring n by this method. Show that it is easier to factor 3 · 901 than to factor 901. 4. Rosen 3.7 #11, pg. 139 Find all integer solutions of each of the following linear diophantine
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Unformatted text preview: equations: ( a ) 2 x + 3 y + 4 z = 5 ( b ) 7 x + 21 y + 35 z = 8 ( c ) 101 x + 102 y + 103 z = 1 . 5. Rosen 3.7 #16, pg. 139 A piggy bank contains 24 coins, all of which are nickels, dimes, or quar-ters. If the total value of the coins is two dollars, what combinations of coins are possible? 6. Rosen 3.7 #22, pg. 140 The post oﬃce of Davis is left with stamps of only two values. They discover that there are exactly 33 postage amounts that cannot be made up using these stamps, including 46 cents. What are the values of the remaining stamps? 1...
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