MathDB

Koshchey opened an account at the bank. Initially, it had 0 rubles. On the first day, Koshchey puts

k>0

rubles in, and every next day adds one ruble more there than the day before. Each time after Koshchey deposits money into the account, the total amount in the account is divided by two by the bank. Find all such

k{}

for which the amount on the account will always be an integer number of rubles.
Proposed by S. Berlov

Problem Statement