MathDB

There are

n{}

currencies in a country, numbered from 1 to

n{}.

In each currency, only non-negative integers are possible amounts of money. A person can have only one currency at any time.
A person can exchange all the money he has from currency

i{}

to currency

j{}

at the rate of

\alpha_{ij}

which is a positive real number. If he had

d{}

units of currency

i{}

he instead receives

\alpha_{ij}d

units of currency

j{}

while this number is rounded to the nearest integer; a number of the form

t-1/2

is rounded to

t{}

for any integer

t{}.

It is known that

\alpha_{ij}\alpha_{jk}=\alpha_{ik}

and

\alpha_{ii}=1

for every

i,j,k.

Can there be a person who can get rich indefinitely?
Proposed by I. Bogdanov

Problem Statement