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Beatty's theorem in rings of integers?
Posted:
Jul 5, 1996 6:35 PM
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Beatty's theorem states that if a and b are positive irrational numbers
satisfying 1/a + 1/b = 1, then {floor(na) | n in N} and {floor(nb) | n in N}
partition the positive integers N into two disjoint sets. Is there a
generalization of this to rings of algebraic integers? It is not even
clear to me how to formulate the question precisely, but something like
this seems to be what I need for another problem I'm working on.
--
Tim Chow tchow@umich.edu
Where a calculator on the ENIAC is equipped with 18,000 vacuum tubes and weighs
30 tons, computers in the future may have only 1,000 vacuum tubes and weigh
only 1 1/2 tons. ---Popular Mechanics, March 1949
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