The Fibonacci sequence goes F(0)=0, F(1)=1, and for n>1, F(n)=F(n-1)+F(n-2).

Show that for every positive integer m there exists an integer n>0 such that m divides F(n).

(In reply to Clueless by Steve Herman)

Thanks.  I submitted this as a contest problem in 2003.  Would you believe that unlimited precision mathematics software found that the first Fibonacci number divisible by 2003 is F(860)?

Posted by McWorter on 2005-06-11 15:48:04