روشي نو براي محاسبه عدد فرابنيوس

A New Approach for Calculating Frobenius Number

In old times some countries used to coin their coins in the bases of prime numbers and people, as an entertainment, were trying to find out " the most amount that can not be payed with the combination of the belonging coins". This number is know as the Frobenius number. More precisely, let Ak = al ,..., ak } be a set of natural numbers such that {a0, ,al,...,ak}=1 .Then the natural number N has a representation in the bases of Ak , if there exist {x0, x1 , rk E No = N U {o} such that N=xoao +xlal +...+xkak. Now, the largest number, which can not be represented in the above form is called the Frobenius number. In the present paper we try to give a new technique for the calculation of the Frobenius number for certain sets.