Number theory : step by step /
"This book examines the patterns and beauty of positive integers by using elementary methods. It discusses some of the outstanding problems which have not been resolved even after hundreds of years of trying. A challenging problem, even for powerful computers, is factorizing integers and the bo...
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| Main Author: | |
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| Format: | Printed Book |
| Language: | English |
| Published: |
Oxford :
Oxford University Press,
2020
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| Subjects: | |
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| LEADER | 02150cam a2200205 i 4500 | ||
|---|---|---|---|
| 008 | 191121s2020 enka b 001 0 eng | ||
| 020 | |a 9780198846734 | ||
| 082 | |2 23 |a 512.7 | ||
| 100 | 1 | |a Kuldeep Singh |9 1591532 | |
| 245 | 1 | 0 | |a Number theory : |b step by step / |c Kuldeep Singh |
| 260 | |a Oxford : |b Oxford University Press, |c 2020 | ||
| 300 | |a xi, 385 pages : |b illustrations (some color) ; |c 25 cm. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "This book examines the patterns and beauty of positive integers by using elementary methods. It discusses some of the outstanding problems which have not been resolved even after hundreds of years of trying. A challenging problem, even for powerful computers, is factorizing integers and the book highlights some methods that are used to simplify this. We factorize integers of the type and solve the equivalent non - linear Diophantine equation where p is prime. To see if such equations have integer solutions, we use the 'Law of Quadratic Reciprocity' which is one of the most powerful results in number theory. The methods of factorization use a new arithmetic called 'clock arithmetic' which also helps in finding the last few digits of a large number without writing down all the digits. The book applies clock arithmetic to test whether a given number is prime or composite. We conclude by showing one of the great results of mathematics that a prime number which leaves a reminder of one after dividing by four can be written as the sum of two squares. However, a prime number which leaves a reminder of three after dividing by four cannot be written as the sum of two squares. Most of the results in the book are placed in an historical context"-- | ||
| 650 | 7 | |2 fast |9 1103370 |a Number theory | |
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| 942 | |2 ddc |c BK | ||
| 955 | |b xd04 2019-11-21 |a xn11 2021-05-06 1 copy rec'd., to USASH |a rl00 2021-05-14 to SMA |c rl13 2021-12-09 to rl12 for rev | ||
| 999 | |c 381243 |d 381243 | ||
| 952 | |0 0 |1 0 |2 ddc |4 0 |6 512_700000000000000_KUL_N |7 0 |9 447971 |a UL |b UL |c ST1 |d 2023-02-08 |g 1995.00 |l 1 |o 512.7 KUL/N |p 108061 |r 2023-09-09 |s 2023-08-05 |v 1995.00 |y BK | ||