HW10 - a + 1 and 4 a 2 + 1 are relatively prime. 4. (4...

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EECS 203: DISCRETE MATHEMATICS Homework 9 Due Friday, December 7 at 5pm Put your name and discussion section number (not the meeting time) on the first page of your homework. Submit your homework to (a) CTools, as a PDF file, or (b) the drop box marked “EECS 203” in room EECS 2420. If neither (a) nor (b) is possible please turn in your homework at one of the discussion sections. 1. (4 points) Section 3.5, Problem 8. 2. (4 points) Calculate 3 530 mod 53. Indicate which theorems or properties of modular arithmetic you are using to arrive at an answer. 3. (4 points) Prove that 2
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Unformatted text preview: a + 1 and 4 a 2 + 1 are relatively prime. 4. (4 points) Consider the following procedure that purportedly nds the greatest common divisor of x and y , x > y . FindGCD( x, y ) If y | x return y Else return FindGCD( x, x mod y ) Is this procedure correct? If so, is it signicantly faster or slower than Euclids algorithm? If not correct, why not? 5. (4 points) The Fibonacci numbers are dened recursively as: F = 1 F 1 = 1 F n = F n-1 + F n-2 , for n > 1 Prove that for all n > 0, F n and F n-1 are relatively prime. 1...
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