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 Unusual binary representation (Posted on 2005-06-14)
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 No Rating

 Subject Author Date re: a slightly different proof Bob Smith 2005-06-21 01:21:27 a slightly different proof Paul 2005-06-18 01:46:25 prove armando 2005-06-15 14:18:44 Proof (Based on what was said earlier) Gamer 2005-06-15 02:14:45 re(2): Negabinary Richard 2005-06-15 01:48:53 re: Negabinary Old Original Oskar! 2005-06-15 00:09:14 Negabinary Richard 2005-06-14 21:54:24 Answer e.g. 2005-06-14 20:18:19 No Subject Jer 2005-06-14 17:03:51

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