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Omni-MATH / The writer Arthur has n≥1 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 …

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problem

The writer Arthur has n≥1n \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 nn Fibonacci numbers (defined by F1=F2=1F_1 = F_2 = 1 and Fk+2=Fk+1+FkF_{k+2}= F_{k+1} + F_k). For which nn is it possible that none of the co-authors had a lapse of memory?
Plain-text mathematical notation (without MathML)
The writer Arthur has n≥1 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 F₁=F₂=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?
Original LaTeX notation
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?

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task_id
bf65e884-8295-5df6-ae73-233e6c439f3f
task_key
test--bf65e884-8295-5df6-ae73-233e6c439f3f
task_revision_id
1
config / split
/ test

Official source

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