CMSC 250 Lecture Notes - Lecture 10: Modular Arithmetic, Mathematical Induction

• School: University of Maryland
• Department: Computer Science
• Course: CMSC 250
• Professor: William Gasarch

Document Summary

M divides (a-b) means that m is a factor of (a-b) If you still have no idea what i"m talking about, just think of it as: we are taking a large. A sequence is a collection of object in which repetition is allowed. Examples include: (cid:883),(cid:883),(cid:883),(cid:883),(cid:883), , (cid:883),(cid:884),(cid:885),(cid:886),(cid:887),(cid:888), , (cid:884), (cid:885), (cid:886), , (cid:1853)=(cid:884), (cid:1866)=(cid:882),(cid:883),(cid:884), (cid:883), (cid:1866)=(cid:882),(cid:883) It is denoted with the greek letter (cid:1853). This tell you to sum up all the data. So if we have the sum of the first 100 numbers, it would look something like this: Don"t worry about where the formula comes from. But the formula works and there is a proof for it. Having said that, the sum of the first one hundred numbers is. This category is perhaps the most important category you will learn in this course so pay attention closely. Suppose we want to prove that a postulate (cid:1868)(cid:4666)(cid:1866)(cid:4667) is true for all natural numbers (cid:1866).