Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In this paper, the problem of the computation of infpp over the set of exponent pairs under linear constrains for a certain class of objective functions is considered and an eective algorithm is presented.
Abstract: We consider the problem of the computation of infpp over the set of exponent pairsP3p under linear constrains for a certain class of objective functions . An eective algorithm is presented. The output of the algorithm leads to the improvement and establishing new estimates in the various divisor problems in the analytical number theory.
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08 Dec 1993
TL;DR: In this article, a method and apparatus for performing integer and floating-point divide operations using a single modified SRT divider 30 in a data processor 10 is presented, where the floating point and integer division are performed using SRT division on normalized positive mantissas (divided and divisor), however, the sequence of operations is modified during the performance of an integer divide operation.
Abstract: A method and apparatus for performing integer and floating-point divide operations using a single modified SRT divider 30 in a data processor 10. The floating-point and integer division is performed using SRT division on normalized positive mantissas (divided and divisor). Integer division shares portions of the floating point circuitry, however, the sequence of operations is modified during the performance of an integer divide operation. The SRT divider 30 performs a sequence of operations before and after an iteration loop to re-configure an integer divisor and dividend into a data path representation which the SRT algorithm requires for floating-point mantissas. During the iteration loop, quotient bits are selected and used to generate intermediate partial remainders. The quotient bits are also input to quotient registers 66 which accumulate the final quotient mantissa. A full mantissa adder is used to generate a final remainder.
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TL;DR: Garcia and Voloch as mentioned in this paper showed that the constant 4 in their bound can be replaced by 3\cdot 2^{-2/3] for the Fermat equation.
Abstract: In 1988 Garcia and Voloch proved the upper bound 4n^{4/3}(p-1)^{2/3} for the number of solutions over a prime finite field F_p of the Fermat equation x^n+y^n=a, where a \in F_p^* and n \ge 2 is a divisor of p-1 such that (n-1/2)^4 \ge p-1. This is better than Weil's bound p+1+(n-1)(n-2)p^{1/2} in the stated range. By refining Garcia and Voloch's proof we show that the constant 4 in their bound can be replaced by 3\cdot 2^{-2/3}.
01 Jan 2000
TL;DR: A sieving algorithm which enumer- ates primes in the interval (x1 ;x 2), using O(x 1=3 2 )b its of memory and using O (x2 x1 + x 1 =3 2) arithmetic operations on numbers of O(ln x2) bits is described.
Abstract: We describe a \dissected" sieving algorithm which enumer- ates primes in the interval (x1 ;x 2), using O(x 1=3 2 )b its of memory and using O(x2 x1 + x 1=3 2 ) arithmetic operations on numbers of O(ln x2) bits. This algorithm is based on a recent algorithm of Atkin and Bern- stein (1), modied using ideas developed by Voronofor analyzing the Dirichlet divisor problem (20). We give timing results which show our algorithm has roughly the expected running time.
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TL;DR: In this article, in cyclic units group G_k = A_k B_k mod p^k, coprime to p, of order (p-1)p^{k-1}.
Abstract: Primitive roots of 1 mod p^k (k>2 and odd prime p) are sought, in cyclic units group G_k = A_k B_k mod p^k, coprime to p, of order (p-1)p^{k-1}. 'Core' subgroup A_k has order p-1 independent of k, and p+1 generates 'extension' subgroup B_k of all p^{k-1} residues 1 mod p. Divisors r,t of powerful generator p-1=rs=tu of \pm B_k mod p^k, and of p+1, are investigated as primitive root candidates. Fermat's Small Theorem: x^{p-1} \e 1 mod p for 0 2}. And for prime p: 2^p !=2 and 3^p != 3 (mod p^3). Re: Wieferich primes [4] and FLT case_1. Conj: at least one divisor of p \pm 1 is a semi primitive root of 1 mod p^k. -- (paper withdrawn, re thm2.2)