We consider the replenishment routing problems of one supplier who can replenish only one of multiple retailers per period, while different retailers need different periodical replenishment. For simple cases satisfying certain conditions, we obtain the simple routing by which the supplier can replenish each retailer periodically so that shortage will not occur. For complicated cases, using number theory, especially the Chinese remainder theorem, we present an algorithm to calculate a feasible routing so that the supplier can replenish the selected retailers on the selected periods without shortages. 相似文献
Matrix scaling is the problem of assigning values to the elements of a matrix that are proportional to a given input matrix. The assignment should fulfill a set of row- and column-sum requirements. We propose a new method that differs from divisor-type methods appeared until now in the literature. This method combines the largest remainder apportionment and bi-proportional rounding. Exhaustive application to the Greek parliamentary elections of 2007 justify our effort. 相似文献
Quantitative estimates for the remainder terms in the asymptotic summation of linear difference systems are derived. For example, it is shown that any decay in excess of summability is passed on to the remainder. 相似文献
We propose a class assignment where students are asked to construct and implement an efficient algorithm to calculate the last digits of a positive integral power of a positive integer. The mathematical prerequisites for this assignment are very limited: knowledge of remainder calculus and the binary representation of a positive integer. The periodicity of the last digits is studied by means of the Euler totient function and the Carmichael function. 相似文献
Define to be the smallest strong pseudoprime to all the first prime bases. If we know the exact value of , we will have, for integers , a deterministic primality testing algorithm which is not only easier to implement but also faster than either the Jacobi sum test or the elliptic curve test. Thanks to Pomerance et al. and Jaeschke, are known for . Upper bounds for were given by Jaeschke.
In this paper we tabulate all strong pseudoprimes (spsp's) to the first ten prime bases which have the form with odd primes and There are in total 44 such numbers, six of which are also spsp(31), and three numbers are spsp's to both bases 31 and 37. As a result the upper bounds for and are lowered from 28- and 29-decimal-digit numbers to 22-decimal-digit numbers, and a 24-decimal-digit upper bound for is obtained. The main tools used in our methods are the biquadratic residue characters and cubic residue characters. We propose necessary conditions for to be a strong pseudoprime to one or to several prime bases. Comparisons of effectiveness with both Jaeschke's and Arnault's methods are given.