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Vô Conjecture 39(VC39): A Height–Radical Density Problem for Linear Equations over Number Fields
We formulate two density conjectures for non-degenerate solutions of the linear equation x1+⋯+xn=0 over the ring of integers of an arbitrary number field. The solutions are selected by an inequality relating their projective height to an ideal-theoretic radical, defined using prime ideals at which the valuations of the coordinates are not all equal.
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