It all began with problem 19408 (problem 8 from Tangente 194, page 49, 2020), taken from the 2012 International Mathematical Games Championship…! Here is the problem.
Sequences defined by linear recurrences
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The solution given on page 51 was somewhat obscure, and this article offers a good opportunity to shed some light on it. We shall focus primarily on the sequence M(n), which obeys a linear recurrence relation. It is "linear" because each term is a linear combination of several preceding terms.
The simplest linear recurrence relation, of order 1, has the form
