% operator (was Re: count of bits set in a long)

[Georg Wittig]

tac at cs.brown.edu (Theodore A. Camus) writes:

>However, 077 in octal is 63 in decimal, and I believe the following
					     ^^^^^^^^^
>relationship is true : x % 63 = [(x % 64) + (x / 64)] % 63

	Does there exist a proof for that equation? Can it be found in
	literature? Is the following true?
	
		x % n = (x%(n+1) + floor(x/(n+1))) % n	      (n != 0;n != -1)
	
	Do there exist similar "surprising" equations?
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