Unformatted text preview: On = {1,3, . .., 2n1}. Note that it follows that O is the set of odd numbers. (b) Prove that O = S . (Recall that this means you have to prove that S is a subset of; O and O is a subset of S . To show that S is a subset of O , use the fact that S is the smallest set satisfying S1 and S2. To show that O is a subset of S , prove by induction that On is a subset of S .) 3. [5 points] Define a function h inductively as follows. { h(1) = h(2) = 1 { h(n) = h(n1)^2 + h(n2) if n > 2. The function h grows quickly after the first few values. (a) Compute h(5). (b) Prove that for all n > 1 that the greatest common divisor of h(n) and h(n1) is 1 (i.e., h(n) and h(n1) are relatively prime). (Hint: induction is a good approach here). Page 1 of 1 Computer Science 280: Homework 3 10/18/2008 http://www.cs.cornell.edu/courses/cs280/2008sp/280hw3.html...
View
Full Document
 Spring '07
 SELMAN
 Computer Science, Natural number, Prime number, Greatest common divisor, Divisor

Click to edit the document details