What This Document Is
This document contains solutions to the tenth homework assignment for Carnegie Mellon University’s Great Theoretical Ideas In Computer Science (15-251) course, Fall 2015. It is a completed assignment intended for review and self-assessment. A writing session was scheduled shortly after the homework due date.
Why This Document Matters
This document is valuable to students who took 15-251 in Fall 2015 and are reviewing their work, or to those studying the course materials independently. It provides worked solutions to problems covering the greatest common divisor (GCD), Euclid’s Algorithm, modular arithmetic, and Fibonacci numbers.
Common Limitations or Challenges
This document provides *answers* to the homework problems, but does not offer explanations of the underlying concepts. It assumes familiarity with the course material and is not a substitute for attending lectures or reading the textbook. It is specifically tailored to the Fall 2015 iteration of the course.
What This Document Provides
The full document includes detailed solutions for the following problems:
* Proofs relating GCD properties and Euclid’s Algorithm.
* An analysis of the time complexity of Euclid’s Algorithm.
* Proofs regarding multiples of the GCD.
* A modified version of Euclid’s Algorithm to find coefficients *k* and *l* such that *kA + lB = gcd(A, B)*.
* An explanation of how to compute modular inverses.
* A discussion of “Fibtorials” and related binomial coefficient analogues.
This preview does *not* include the actual solutions or proofs themselves. It only describes the topics covered.
