Abstract: In this paper, we use
the theory of Boolean functions to find a new elementary proof for Moser’s
conjecture that states that in the bounded sequence of nonnegative integers
divisible by 3 there are more integers with an even number of 1s in their base-2
representation. This proof is simpler than the original proof by Newman in [5].
We further apply the method to prove a similar result for
Keywords and phrases: Boolean functions, Thue-Morse sequence, Binary representation.
