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Wed 14 Sep, 2005 07:03 pm
Hi all! I need to:
Show that every nonzero integer can be uniquely represented in the form:
e_k*3^k + e_(k-1)*3^(k-1) + . . . + e_1*3 + e_0
where e_j = -1, 0, or 1 for j = 0, 1, 2, . . . , k and e_k is not equal to zero. This expansion is called a balanced ternary expansion.
Thanks!
I'd guess that you need to demonstrate a bijection between ternary and balanced ternary.
Note the following relationships:
ternary --- balanced ternary
0 = 0
1 = 1
2 = 1 -1
I this is a base three expansion even though one of the base numbers is negative. Like all other bases, any integer will be uniquely represented.
See
balanced ternary
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