Hmk3 - 2n+1 + 2 n+2 ) for all integers n 0. 7) Using...

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COT 3100 Homework # 3 Spring 2000 Assigned: 2/15/00 Due: 3/2,3 in recitation 1) Use Euclid’s Algorithm to find the greatest common divisor(GCD) of 87 and 57. 2) Show that if 7 | 3x + 4y, then there are no integer solutions to the equation 23x + 26y = 20000 3) Prove that if 3 | x + 4y, then 12 | 20x + 44y. 4) Using mod rules, find the remainder when you divide 7 200 by 9. 5) Let a and b be two positive integer. If a is odd, show that 7ab + 3b 2 is even. 6) Using induction, prove that 7 | (3
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Unformatted text preview: 2n+1 + 2 n+2 ) for all integers n 0. 7) Using induction, show the following: = +-n i i i i 1 ) 1 )( 1 ( = (n-1)n(n+1)(n+2)/4 8) Use induction to show that 3 n < n! for all integers n > 6. 9) The Fibonacci numbers are defined as follows: F 1 = F 2 = 1, and F n = F n-1 + F n-2 , for all integers n > 2. Prove the following closed summation closed form using induction: = n i i F 1 = F n+2 1, for integers n > 0....
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This document was uploaded on 07/14/2011.

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