The strong Goldbach conjecture states that every even integer greater than two is the sum of two primes. The weak Goldbach conjecture is very similar, instead modifying the sum from two primes to three primes.
The prime numbers are on example of a series, as is the Fibonacci series. Extending the Goldbach conjecture idea to the Fibonacci series, I am wondering about the status of this statement:
For every (even/odd) integer greater than K, it can be rewritten as the sum of N Fibonacci numbers (N and K are constant)
Extra: the Fibonacci series is simply one type of series that can be extended to the Goldbach conjecture idea. Are there any other special series that are true or false to this idea?
I am trying to explore the mathematics behind this baffling conjecture. All help is appreciated, Thank you.