If there is, it must be greater than 276792026060022456497058911697376830627911091457539277300827264605865506146172478305720990198054221114105111525234958335011060935983844946443475003682525687205923438462532622519320479701851802392 This is the smallest number that is not a Fibonacci number that is not excluded by this modulus: 5752028405020859396395768625940010545359026815479616133477751814335827064308752092084424225510402022972844755481554083297677086937356202818322021388807601850180058538115156217193711471626944740035227 I suspect there's a simple proof that there is no such number. Raising the limit above is straightforward; that's from a few minutes of CPU time. -tom On Thu, Oct 8, 2020 at 8:07 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?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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