MathDB

The writer Arthur has

n \ge1

co-authors who write books with him. Each book has a list of authors including Arthur himself. No two books have the same set of authors. At a party with all his co-author, each co-author writes on a note how many books they remember having written with Arthur. Inspecting the numbers on the notes, they discover that the numbers written down are the first

n

Fibonacci numbers (defined by

F_1 = F_2 = 1

and

F_{k+2}= F_{k+1} + F_k

). For which

n

is it possible that none of the co-authors had a lapse of memory?

Problem Statement