No Fibonacci number is congruent to 4 or 6 mod 8. See http://oeis.org/A066853 (the sequence that gives the number of "Fibonacci residue classes" mod m for m=1,2,3,...) and http://oeis.org/A079002 (the sequence of moduli such that the Fibonacci numbers fill all m possible residue classes). Jim On Fri, Oct 9, 2020 at 8:10 AM Allan Wechsler <acwacw@gmail.com> wrote:
Perhaps I have misunderstood how the quantifiers are scoped an this question. I recall being convinced that the Fibonacci numbers hit all residue classes, in which case every integer is "pseudo-Fibonacci". If this is not true, can you name a residue class that contains no Fibonacci numbers?
On Thu, Oct 8, 2020, 11:07 PM James Propp <jamespropp@gmail.com> wrote:
Does there exist a positive integer n that isn’t a Fibonacci number, such that for every modulus m there is a Fibonacci number congruent to n mod m?
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