Question

We define the sequence of numbers

an =
1 if 0 <=n <=3 and
an-1 + an-2 + an-3 + an-4
, if n >= 4.
Prove that an =1 (mod 3) for all n >= 0.

Answer 1

a6 = 11+2 = 13 = 1 mod 3

each term is 1 mod 3 ... so it's (1 + 1 + 1 + 1) mod 3 = 1 mod 3 ... something like that