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Date: 19-1-2020
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Date: 8-11-2020
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Date: 23-11-2020
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Vorobiev's theorem states that if , then
, where
is a Fibonacci number and
means
divides
. The theorem was discovered by Vorobiev in 1942, but not published until 1967. It was used by Y. Matiyasevich in his negative solution to the Hilbert's tenth problem.
Note that the converse does not hold. For example, , but
. The plot above shows values of
for which
and
(black) and for which
but
(red).
REFERENCES:
Vorobiev, N. N. Fibonacci Numbers. Basel, Switzerland: Birkhäuser, 2002.
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