MathDB

A machine accepts coins of

k{}

values

1 = a_1 <\cdots < a_k

and sells

k{}

different drinks with prices

0<b_1 < \cdots < b_k

. It is known that if we start inserting coins into the machine in an arbitrary way, sooner or later the total value of the coins will be equal to the price of a drink. For which sets of numbers

(a_1,\ldots,a_k;b_1,\ldots,b_k)

does this property hold?

Problem Statement