Math number theory proof question.?

E

Evan

New member
Prove that each positive integer n has a unique representation as a finite sum of distinct non-negative integer powers of two. For example, 5 = 1 + 4 is the unique sum of distinct powers of 2 for 5. 5 = 1.+ 2 + 2, but that doesn't count as 2 is used twice. I know what these sums represent, but I'd be interested in a proof of this statement.
 
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