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Unusual binary representation (Posted on 2005-06-14) Difficulty: 3 of 5
Show that every positive integer is an alternating sum of strictly increasing powers of 2.

For example, 5=2^0 -2^2 +2^3 and 8=-2^3 +2^4 are alternating sums of strictly increasing powers of 2 (8=2^3 is ok too).

10=-2^1 -2^2 +2^4 is a strictly increasing sum but not alternating.

4=2^1 -2^1 +2^2 is alternating but not strictly increasing.

(author: prof Dan Shapiro of Ohio State University)

See The Solution Submitted by McWorter    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: a slightly different proofBob Smith2005-06-21 01:21:27
Solutiona slightly different proofPaul2005-06-18 01:46:25
provearmando2005-06-15 14:18:44
SolutionProof (Based on what was said earlier)Gamer2005-06-15 02:14:45
re(2): NegabinaryRichard2005-06-15 01:48:53
Some Thoughtsre: NegabinaryOld Original Oskar!2005-06-15 00:09:14
NegabinaryRichard2005-06-14 21:54:24
Some ThoughtsAnswere.g.2005-06-14 20:18:19
No SubjectJer2005-06-14 17:03:51
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