Question

8 marks] Number representations. We define the predicate BT(n,): "r has a balanced ternary represen tation that contains n digits," where n eZ+ and z e Z. Equivalently BT(n,z) : 34, di, ,dn-le(-1,0,1), Σdi.gi=z Prove the following statement using induction on n 3a-1

Answer 1

Base-case-of 2. втск, x) 、hald. Jr.ee ナ1 t-v such that K+ 2 2.

2 82 Ren.co.an-futカン .dk-O., dese add na , can ·tgzeugty加 get BT(kthx)、 2 2

k+f ftbre adg do, d) _ _.dk-i MX、st Similarty for