On a problem of Frobenius
β Scribed by Pamela A Ferguson
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 518 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let X k =[a 1 , a 2 , ..., a k ], k>1, be a subset of N such that gcd(X k )=1. We shall say that a natural number n is dependent (on X k ) if there are nonnegative integers x i such that n has a representation n= k i=1 x i a i , else independent. The Frobenius number g(X k ) of X k is the greatest i
Suppose \(a, b, c\) are three positive integers with \(\mathrm{gcd}=1\). We consider the function \(f(a, b, c)\) defined to be the largest integer not representable as a positive integral linear combination of \(a, b, c\). We give a new lower bound for \(f(a, b, c)\) which is shown to be tight, and
concerning the well-known diophantine problem of Frobenius was given an exact solution for linear forms with the set of coefficients of density 1 2 (or more). In the present paper, we advance this up to the density 1 3 .
Two celebrated applications of the character theory of finite groups are Burnside's p β£ q β€ -Theorem and the theorem of Frobenius on the groups that bear his name. The elegant proofs of these theorems were obtained at the beginning of this century. It was then a challenge to find character-free proo
The Diophantine Problem of Frobenius is to find a formula for the least integer not representable as a nonnegative linear form of positive integers. A reduction formula for the Diophantine Problem of Frobenius is presented. The formula can be applied whenever there are common divisors of the coeffic