Common Values of Padovan and Perrin Sequences.

The integer sequence defined by P n + 3 = P n + 1 + P n with initial conditions P 0 = P 1 = P 2 = 1 is known as the Padovan sequence (P n) n ∈ Z . The Perrin sequence (R m) m ∈ Z satisfies the same recurrence equation as the Padovan sequence but with starting values R 0 = 3 , R 1 = 0 , and R 2 = 2 . In this note, we solve the Diophantine equation P n = ± R m with (n , m) ∈ Z 2 . [ABSTRACT FROM AUTHOR]