In the Year 2525

The song wonders, “In the year 2525, if man is still alive . . . “

In what year must man be alive to hear the cicadas and see Halley’s comet in the same year?

The cicadas appeared in 1987 and return every 17 years.
Halley’s Comet last appeared in 1986 and returns every 76 years.

Cicada on a person's fingerNasa photo of Halley's Comet in 1986
Cicada every 17 years . . . . . . . . . . . . . . . . . . . . . . . . Halley’s Comet every 76 years

Will they ever be together again?

Answer
Brute Force:

Create two series in Excel for the two events. Then creatively prune the columns and visually find entries in the two columns that match.
Diophantine Solution:
Given that 1986 + 76i = 1987 + 17j
Simplifying 76i –17j = 1
See Diophantine example for technique used to solve equation. i = 15 + 17m where m = any integer
j = 67 + 76m where m = any integer
When m = 0, i = 15 and j = 67. Halley’s comet will appear in 1986 + 76 * 15 = 3126
Doublecheck:
1987 + 17 * 67 = 3126. The cicadas will appear that year too.

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