Question 6
I 6 (ROM 4), IMO3
Does there exist a natural number $n$ for which the number
$$\sum_{k=0}^n\binom{2n+1}{2k+1}2^{3k}$$
is divisible by $5$?
Does there exist a natural number $n$ for which the number
$$\sum_{k=0}^n\binom{2n+1}{2k+1}2^{3k}$$
is divisible by $5$?