MathDB

For each positive integer

n

, let

a_n = 0

(or

1

) if the number of

1

’s in the binary representation of

n

is even (or odd), respectively. Show that there do not exist positive integers

k

and

m

such that

a_{k+j}=a_{k+m+j} =a_{k+2m+j}

for

0 \leq j \leq m-1.

Problem Statement