MathDB

Each of

N

people chooses a random integer number between

1

and

19

(including

1

and

19

, and not necessarily with the same distribution). The random numbers chosen by the people are independent from each other, and it is true that each person chooses each of the

19

numbers with probability at most

99\%

. They add up the

N

chosen numbers, and take the remainder of the sum divided by

19

. Prove that the distribution of the result tends to the uniform distribution exponentially, i.e. there exists a number

0<c<1

such that the mod

19

remainder of the sum of the

N

chosen numbers equals each of the mod

19

remainders with probability between

\frac{1}{19}-c^{N}

and

\frac{1}{19}+c^{N}

Problem Statement