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Local-global principle for quadratic forms over fraction fields of two-dimensional henselian domains

Yong HU (2012)

Annales de l’institut Fourier

Let R be a 2-dimensional normal excellent henselian local domain in which 2 is invertible and let L and k be its fraction field and residue field respectively. Let Ω R be the set of rank 1 discrete valuations of L corresponding to codimension 1 points of regular proper models of Spec R . We prove that a quadratic form q over L satisfies the local-global principle with respect to Ω R in the following two cases: (1) q has rank 3 or 4; (2) q has rank 5 and R = A [ [ y ] ] , where A is a complete discrete valuation ring with...

Lucas balancing numbers

Kálmán Liptai (2006)

Acta Mathematica Universitatis Ostraviensis

A positive n is called a balancing number if 1 + 2 + + ( n - 1 ) = ( n + 1 ) + ( n + 2 ) + + ( n + r ) . We prove that there is no balancing number which is a term of the Lucas sequence.

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