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Tag Archives: proof

Multiples in the Fibonacci series

I found the following problem on K. Rustan M. Leino’s puzzles page:

[Carroll Morgan told me this puzzle.]
Prove that for any positive K, every Kth number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.
More formally, for any natural number n, let F(n) denote Fibonacci number n. That is, F(0) [...]