olymmath

BALTIC-WAY 2006 Problem 1

  • Answer

For a sequence a1,a2,a3,…a_{1}, a_{2}, a_{3}, \ldots of real numbers it is known that

an=an−1+an+2 for n=2,3,4,…a_{n}=a_{n-1}+a_{n+2} \text { for } n=2,3,4, \ldots

What is the largest number of its consecutive elements that can all be positive?

Dataset text NuminaMath olympiads. Quoted with source.

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