## Exponential and Logarithmic Functions Review

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AP Notes, Outlines, Study Guides, Vocabulary, Practice Exams and more!

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The Zsigmondy Theorem PISOLVE 7/31/11 Abstract In this paper we will be discussing the uses and applications of Zsigmondy?s Theorem. As some of you may consider the theorem as ?large/ brutal? , it can actually be proved by elementary methods [1] - at the same time, it is applicable in so many Number Theoretic problems(All problems in this article are sourced in AoPS). We see no reasons not to use it. Intro Problem Let p > 3 be a prime. Show that every positive divisor of 2 p+1 3 is in the form 2kp+ 1. Solution: We show that all prime divisors are in this form, then the result readily follows.Let q| 2 p+1 3 . Then: q|22p ? 1 o2(q)|2p If o2(q) 6= 2p, we have 3 cases: o2(q) = 1 Then q|1, clearly impossible. o2(q) = 2

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? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq

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Basics of Algebra Algebra is a division of mathematics designed to help solve certain types of problems quicker and easier. Algebra is based on the concept of unknown values called variables, unlike arithmetic which is based entirely on known number values. This lesson introduces an important algebraic concept known as the Equation. The idea is that an equation represents a scale such as the one shown on the right. Instead of keeping the scale balanced with weights, numbers, or constants are used. These numbers are called constants because they constantly have the same value. For example the number 47 always represents 47 units or 47 multiplied by an unknown number. It never represents another value.

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