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Topic: Beatty's theorem in rings of integers?
Replies: 1   Last Post: Jul 7, 1996 10:38 AM

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Timothy Chow

Posts: 29
Registered: 12/12/04
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
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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