elementary number theory
Elementary Number Theory: Primes, Congruences, and Secrets pdf
... the University of Washington. The systematic study of number theory was initiated around 300B.C. when Euclid proved that there are infinitely many prime numbers, and also cleverly deduced the fundamental ... communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, public-...
Ngày tải lên: 07/03/2014, 16:20
elementary number theory - clark
... CHAPTER 10. PRIME NUMBERS Theorem 10.1 (Euclid’s Theorem). There are infinitely many prime numbers. Proof. Assume, by way of contradiction, that there are only a finite number of prime numbers, say: p 1 ,p 2 , ... is isprime(n); The following primality test for Mersenne numbers makes it easier to check whether or not M p is prime when p is a large prime. Elementary Number Theory W. Edwi...
Ngày tải lên: 31/03/2014, 16:21
elementary number theory and primality tests
... coprime to n even if n is composite. 5.2 Carmichael numbers Definition 5.2 Suppose n is an odd number > 1. Then we say that n is aCarmichael number if n is not a prime, but is a pseudoprime to ... then m has no proper factors, ie m is prime. Definition 4.1 The numbers M p = 2 p − 1, where p is prime, are called Mersenne numbers. 4–1 374 1–22 Corollary 1.2 If k is a field then k[x] is a...
Ngày tải lên: 31/03/2014, 16:21
elementary number theory notes - santos
... non-negative real numbers there is always one number which is at least the average of the number s and that there is always one member that it is at most the average of the numbers. 81 APS We ... of 3 that divides this number? Solution: By the casting-out-nines rule, this number is divisible by 9 if and only if 19 + 20 + 21 + ···+ 92 = 37 2 · 3 is. Therefore, the number is divisible...
Ngày tải lên: 31/03/2014, 16:21
elementary methods in number theory - nathanson m.b
... and easily understood fact about the natural numbers, then we may want to find another proof, one that uses only elementary arguments” from number theory. Elemen- tary proofs are not better than ... only arithmetic arguments. This book contains elementary proofs of some deep results in number theory. We give the Erd˝os-Selberg proof of the prime number theorem, Linnik’s solution of...
Ngày tải lên: 31/03/2014, 16:21
Tài liệu Frontiers in Number Theory, Physics, and Geometry II docx
... forms, P. Di Vec- chia on Gauge theory and D-branes, E. Frenkel on Vertex algebras, algebraic curves and Langlands program, G. Moore on String theory and number theory, C. Soul´e on Arithmetic ... domains: 1. Dynamical Systems, Number theory, and Random matrices, with lectures by E. Bogomolny on Quantum and arithmetical chaos, J. Conrey on L-functions and random matrix theory, J C...
Ngày tải lên: 12/02/2014, 16:20