Factoring Odd Integers without Multiplication and Division
نویسنده
چکیده
A method of determining two factors of an odd integer without need of multiplication or division operation in iterative portion of computation is presented. It is feasible for an implementing algorithm to use only integer addition and subtraction throughout. Presentation of material is non-theoretical; intended to be accessible to a broader audience of non academic and theoretical practitioners.
منابع مشابه
Factoring in Quadratic Fields
This is closed under addition, subtraction, multiplication, and also division by nonzero numbers. Similarly, set Z[ √ d] = {a+ b √ d : a, b ∈ Z}. This is closed under addition, subtraction, and multiplication, but not usually division. We will define a concept of “integers” for K, which will play the same role in K as the ordinary integers Z do in Q. The integers of K will contain Z[ √ d] but m...
متن کاملHide and Seek-a Naive Factoring Algorithm
Let N be a positive integer that we wish to factor. Say N = UV where U and V are positive integers, not necessarily prime, with 1 < U < V . For simplicity, assume V < 2U , so that V < (2N). The general case, without this restriction, will be handled at the end of this section. The idea behind the algorithm is to perform trial division of N by a couple of integers, and to use information about t...
متن کاملUsing Lucas Sequences to Factor Large Integers near Group Orders
Factoring large integers into primes is one of the most important and most difficult problems of computational number theory (the twin problem is primality testing [13]). Trial division, Fermat's algorithm [1], [3], [8], Pollard's p-\ method [6], Williams' p + \ method [11], Lenstra's elliptic curve method (ECM) [5], Pomerance's quadratic sieve (QS) [7], [10], and Pollard's number field sieve (...
متن کاملFactoring Integers Using the Web
This note provides background on the www-factoring project, which was started in the fall of 1995. Factoring a positive integer ri means finding two positive integers u and v such that the product of u and v equals ri, and such that both u a.nd v are greater than 1. Such u and v are called factors (or divisors) of ii, and n = u v is called a factorization of n. Positive integers that ca.n be fa...
متن کاملChebyshev Polynomials and Primality Tests
Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1703.00372 شماره
صفحات -
تاریخ انتشار 2017