Show that every nonzero integer can be uniquely expressed as ak3^k + ak−13^(k−1) + · · · + a13 + a0 where ai ∈ {−1, 0, 1} and ak ≠ 0.

Solution for Show that every nonzero integer can be uniquely expressed as a_k3^k + a_k-13^k-1 + · · · + a₁3 + a₀ where a_i ∈ {−1, 0, 1} and a_k ≠ 0.

n This follows from the Division algorithm upon noting that if, after dividing n by 3, we obtain a remainder of 2, we may write

n = 3k + 2 = 3(k + 1) − 1