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In Part I the diophantine equation      G n = w p 1 m 1 ⋯  p t m t {G_n} = wp_1^{{m_1}} \cdots p_t^{{m_t}}       was studied, where      { G n } n = 0 ∞  \{ {G_n}\} _{n = 0}^\infty       is a linear binary recurrence sequence with positive discriminant. In this second part we extend this to negative discriminants. We use the  p -adic and complex Gelfond-Baker theory to find explicit upper bounds for the solutions of the equation. We give algorithms to reduce those bounds, based on diophantine approximation techniques. Thus we have a method to solve the equation completely for arbitrary values of the parameters. We give an application to a quadratic-exponential equation.

Products of prime powers in binary recurrence sequences. II. The elliptic case, with an application to a mixed quadratic-exponential equation