Does there exist a number \(h\) such that for any natural number \(n\) the number \(\lfloor h \times 2021^n\rfloor\) is not divisible by \(\lfloor h \times 2021^{n-1}\rfloor\)?
Do you think that among the four consecutive natural numbers there will be at least one that is divisible a) by 2? b) by 3? c) by 4? d) by 5?
Six sacks of gold coins were found on a sunken ship of the fourteenth century. In the first four bags, there were 60, 30, 20 and 15 gold coins. When the coins were counted in the remaining two bags, someone noticed that the number of coins in the bags has a certain sequence. Having taken this into consideration, could you say how many coins are in the fifth and sixth bags?