Pell and Pell-Lucas numbers as sums of two Jacobsthal numbers
Abstract
We solve the two Diophantine equations Pk=Jn+Jm and Qk=Jn+Jm where Pkk≥0, Qkk≥0 and Jkk≥0 are the sequences of Pell numbers, Pell-Lucas numbers and Jacobsthal numbers, respectively. The main tool is the theory of linear forms in logarithms.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.