Pell Identities

MATH 242 practice problems

Learning Goals: Develop and implement an algorithm to solve a mathematical problem, and interpret your results. Formulate precise mathematical conjectures supported by computational evidence. Explore generalizations of known mathematical ideas.

Your task: Discover three identities involving the Pell numbers.

Due: Friday, March 6, at 5:00pm. Upload your solution as a Mathematica notebook to the Pell Identities assignment on Moodle.

Grading: If you state conjectures supported by your computational evidence, you will earn a Satisfactory grade for each problem.

Need help? Review the notes from class (which are posed on the course web site), talk with your classmates, email Prof. Wright, or visit the help session.

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Problem 1:

Compute (Subscript[P, n]^2)+(Subscript[P, n+1]^2) for various positive integers n. Conjecture an identity, supported by computational evidence.

Problem 2:

Compute (Subscript[P, m])(Subscript[P, n+1])+(Subscript[P, m-1])(Subscript[P, n]) for various positive integers n and m. Conjecture an identity, supported by computational evidence.

Problem 3:

Compute (Subscript[P, n+i])(Subscript[P, n+j])-(Subscript[P, n])(Subscript[P, n+i+j]) for various positive integers n, i, and j. Conjecture an identity, supported by computational evidence.