Can we print n distinct natural numbers such that their sum is not a fibonacci number?

Question

Can we print n distinct natural numbers such that their sum is not a fibonacci number?

for eg if n = 3

then 3 numbers can be 1, 2, 3 since 1+2+3=6 which is not a fibonacci number

Answer 1

Welcome to MSE.

Yes -

By induction:

Can we print a list of 1 number whose sum isn't a Fibonacci number? Yes ( exercise :P )

Now (inductively) say we've built a list with n numbers whose sum is not a Fibonacci number. We want to add a new number to the list. There are infinitely many non-Fibonacci numbers bigger than our current sum. Simply pick a new number so that the sum remains non-Fibonacci.

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I hope this helps ^_^