Chapter 8.5, Problem 19P

There are periodical cicadas with 13-year life cycles and other periodical cicadas with 17-year life cycles. The ones with 13- year life cycles become active adults every 13 years, and the ones with 17-year life cycles become active adults every 17 years. Suppose that one year, both the 13-year cicadas and the 17-year cicadas are active adults simultaneously. Find the next four times that both kinds of cicadas will be active adults simultaneously. Use mathematical terms to describe the next time, and all the times, when both kinds of cicadas will be active adults simultaneously. Explain.