E. Bravo

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math.NT2026

On Brocard's problem with Padovan and Perrin numbers

Eric F. Bravo

The Padovan sequence ${P_{m}}_{m \geq 0}$ is a ternary recurrence sequence with companion polynomial $X^{3} - X - 1$ and initial conditions $P_{0} = P_{1} = P_{2} = 1$ . The Perrin sequence $…

math.NT2026

Cullen and Woodall numbers in Padovan and Perrin sequences

Herbert Batte, Eric F. Bravo, Florian Luca

Let ${P_{n}}_{n \geq 0}$ and ${R_{n}}_{n \geq 0}$ denote the Padovan and Perrin sequences, both satisfying the recurrence $U_{n + 3} = U_{n + 1} + U_{n}$ , but with initial values $P_0 = P_1…