Polynomial Identities

Math 242 practice problems

Name: _________________

Learning Goals: Formulate precise mathematical conjectures supported by computational evidence. Explore generalizations of known mathematical ideas.

Your task: In class, we found the “Fibonacci 3n identity” and the “Fibonacci 5n identity.” Now generalize these ideas to find a “Fibonacci 7n identity.” Specifically, look for an identity of the form (Subscript[F, 7n])=(Subscript[a, 7])(Subscript[F, n]^7)+(Subscript[a, 6])(Subscript[F, n]^6)+(Subscript[a, 5])(Subscript[F, n]^5)+(Subscript[a, 4])(Subscript[F, n]^4)+(Subscript[a, 3])(Subscript[F, n]^3)+(Subscript[a, 2])(Subscript[F, n]^2)+(Subscript[a, 1])(Subscript[F, n]). You might want to consider even and odd n separately. State your identity as a conjecture, and show that your conjecture holds for lots of values of n.

Due: Friday , March 4, at 5:00pm. Upload your solution as a Mathematica notebook to the Polynomial Identities assignment (Moodle link).

Grading: If you state an identity of the requested form supported by your computational evidence, you will earn a Satisfactory grade.

Need help? Review the notes from class, which are posed on the course web site. If you still need help, email Prof. Wright.