MathDB

A sequence of integers

a_0, a_1 …

is called kawaii if

a_0 =0, a_1=1,

and

(a_{n+2}-3a_{n+1}+2a_n)(a_{n+2}-4a_{n+1}+3a_n)=0

for all integers

n \geq 0

. An integer is called kawaii if it belongs to some kawaii sequence. Suppose that two consecutive integers

m

and

m+1

are both kawaii (not necessarily belonging to the same kawaii sequence). Prove that

m

is divisible by

3,

and that

m/3

is also kawaii.

N6