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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
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Transforming a recurrence to the product of two other recurrences
This question deals with sequence:
$$a_0 = 0,\ a_1 = 7, \quad a_{n+2} = 14a_{n+1} - a_n + 6$$
The question is about establishing that $a_n$ is a composite number (except some finite cases).
In one …