Problem

Answer the question in Exercise, where instead of five men and one monkey, there are n men...

Answer the question in Exercise, where instead of five men and one monkey, there are n men and k monkeys, and at each stage the monkeys receive one coconut each.

Exercise

Five men and a monkey are shipwrecked on an island. The men have collected a pile of coconuts that they plan to divide equally among themselves the next morning. Not trusting the other men, one of the group wakes up during the night and divides the coconuts into five equal parts with one left over, which he gives to the monkey. He then hides his portion of the pile. During the night, each of the other four men does exactly the same thing by dividing the pile he finds into live equal parts, leaving one coconut for the monkey, and hiding his portion. In the morning, the men gather and split the remaining pile of coconuts into five parts and one is left over for the monkey. What is the minimum number of coconuts the men could have collected for then original pile?

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