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...
View Full Document
- Fall '07
- Number Theory, Prime number, Greatest common divisor, Discrete Mathematics Homework, discussion section number