Document Type : Research Paper

Authors

• Abbas Taheri ¹
• Saeid Alikhani ²

¹ Department of Electrical Engineering, Yazd University, 89195-741, Yazd, Iran

² Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran

Abstract

A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negative
integers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$. The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called the Frobenius number and is denoted by the symbol
$g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate the Frobenius number. Also we present the sequential form of the new algorithm. A number $\alpha$ has a representation with respect to the numbers $\alpha_1,...,\alpha_n$, if there exist the non-negative
integers $\lambda_1,... ,\lambda_n$ such that $\alpha=\lambda_1\alpha_1+...+\lambda_n \alpha_n$.
The largest natural number that does not have a representation with respect to the numbers $\alpha_1,...,\alpha_n$ is called the
Frobenius number and is denoted by the symbol $g(\alpha_1,...,\alpha_n)$. In this paper, we present a new algorithm to calculate the
Frobenius number. Also we present the sequential form of the new algorithm.

Keywords

• Algorithm
• Frobenius
• Number
• Complexity
• Sequence