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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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gcd of elements of associated binary recurrence sequences

On page 55 of the 3rd edition of Ribenboim's ``The New Book of Prime Number Records'', he defines two associated sequences, $U_n(P,Q)=\left( \alpha^n-\beta^n \right)/\left( \alpha-\beta \right)$ and $ …
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