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

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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 ﬁnds 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 signiﬁcantly faster or slower than Euclid’s algorithm? If not correct, why not? 5. (4 points) The Fibonacci numbers are deﬁned 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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