- Question : Prove that the number
is never divisible by 5.
Prove that $\sum_{i=0}^n2^{3i} \binom {2n+1}{2i+1}$ is never divisible by 5
5
$\begingroup$
combinatorics
binomial-coefficients
-
0Why those tags? – 2011-01-04
-
0A hint (although I haven't tried this in detail): call this number $f(n)$. Then $f(n)$ might satisfy some linear recurrence. Plug integers mod 5 into this recurrence and see what happens. – 2011-01-04
-
0@Michael Lugo, Yup, that approach works. – 2011-01-04
-
0f(n) _has to_ satisfy a linear recurrence, but there are easier ways to do this problem. Again, what have you tried? – 2011-01-04