Nicole Lepaute (1723-1788) was a French astronomer considered one of the "best astronomical computers" of the time. In 1758, she made predictions about the return of Halley's Comet and determined how the gravity of the planets can affect the path of a comet. In 1762, she calculated the exact time of a solar eclipse that would occur in 1764 by making a map of the extent of the eclipse throughout Europe, with intervals of 15 minutes.

In this context, let us now consider the following astronomical problem.

Halley's Comet is undoubtedly one of the best known, named in such way because the English astronomer Halley conjectured that the comets that had appeared in the years 1531, 1607 and 1682 were reappearances of the same and that, therefore, their orbit was completed approximately every 76 years.

1- If the comet appeared in 1759, on how many more occasions has it reappeared between then and today? When will the next appearance be?

2- According to the European Space Agency, the first observation of Halley took place in 239 BC. Indicate the 5 years in which the comet appeared after that date.