By Joseph H. Silverman

ISBN-10: 0321816196

ISBN-13: 9780321816191

A pleasant creation to quantity conception, Fourth version is designed to introduce readers to the general issues and method of arithmetic in the course of the specific research of 1 specific facet—number conception. beginning with not anything greater than simple highschool algebra, readers are progressively resulted in the purpose of actively acting mathematical study whereas getting a glimpse of present mathematical frontiers. The writing is acceptable for the undergraduate viewers and comprises many numerical examples, that are analyzed for styles and used to make conjectures. Emphasis is at the tools used for proving theorems instead of on particular effects.

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**Additional resources for A Friendly Introduction to Number Theory (4th Edition)**

**Sample text**

4. A number L is called a common multiple of m and n if both m and divide L. and is denoted by n The smallest such L is called the least common multiple of m and n LCM(m, n ) . For example, LCM(3,7) 21 and LCM(12,66) 132. (a) Find the following least common multiples. (i) LCM(8,12) (ii) LCM(20,30) (iii) LCM(51,68) (iv) LCM(23,18). = (b) For each of the = LCMs that you computed in (a), compare the value of LCM(m, n ) to the values of m, n, and gcd(m, n) . Try to find a relationship. (c) Give an argument proving that the relationship you found is correct for all m and n.

Third, when we say that n can be written as a product in exactly one way, we do not consider rearrangement of the factors to be a new factorization. For example, 12 and 1 2 = = 2 · 2 · 3 and 12 = 2 · 3 2 · 3 · 2 · 2, but all these are treated as the same factorization. Proof The Fundamental Theorem of Arithmetic really contains two assertions. Assertion 1. The number n can be factored into a product of primes in some way. Assertion 2. There is only one such factorization (aside from rearranging the fac tors).

For exam ple, consider the fact that every number can be factored as a product of primes in exactly one way. ) It's not hard to show, even in the IE-Zone, that every (even) number can be written as a product of IE-primes. But consider the following factorizations: 180= 6 . 30= 10 . 18. 4 Since this book is not a multimedia product, you'll have to use your imagination to supply the appropriate Twilight Zone music. [Chap. 7] Factorization and the Fundamental Theorem of Arithmetic 49 Notice that all of the numbers 6, 30, 10, and 18 are IE-primes.

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