Prove that every nonzero integer can be written in the form _i 3i where the exponents i are distinct non-negative integers. (For example: 42 = 34 3 3 3 2 3 1 , 25 = 33 3 1 + 30 , 17 = 3 3 3 2 3 0 .)

Hint: When writing n, should 30 or 3 0 (or neither) be in the sum? Dont even think about using weak induction.