^{2}q where 'p' and 'q' are different prime numbers. Some of the special years of the Lyrans are 12, 18 and 20. On Lyra III one is a student until reaching a special year immediately following a special year (i.e. on the second year of consecutive special years); one then becomes a master until reaching a year that is the third in a row of consecutive special years; finally one becomes a sage until death, which occurs in a special year that is the fourth in a row of consecutive special years.

Now the questions are:

( i.) When does one become a master?

( ii.) When does one become a sage?

(iii.) How long do the Lyrans live?