Chapter 6.1, Problem 82E

Cicadas. Continuing the discussion in Exercise 81, suppose that a predator of both type A and type B cicadas emerges every 5 years. If the predator also emerged in 2010, when will both types of cicadas and the predator all emerge together again?

81. Cicadas. In addition to avoiding their predators, another advantage of the 13- and 17-year emergence pattern for cicadas is that the two species rarely emerge during the same year to compete for food. Suppose that type A cicada has a 13-year emergence cycle and type B cicada has a 17-year cycle. If both type A and type B cicadas emerged during 2010, when is the next time that both cicadas will emerge during the same year?