Congruence ABC implies ABC

The ABC conjecture of Masser and Oesterle' states that if (a,b,c) are coprime integers with a + b + c = 0, then sup(|a|,|b|,|c|) < c_e (rad(abc))^{1+e} for any e > 0. Oesterle' has observed that if the ABC conjecture holds for all (a,b,c) with 16 | abc, then the full ABC conjecture holds. We extend that result to show that, for every integer N, the "congruence ABC conjecture" that ABC holds for all (a,b,c) with N|abc implies the full ABC conjecture.Comment: 4 pages; to appear, Indag. Mat

Do Magnetic Fields Prevent Hydrogen from Accreting onto Cool Metal-line White Dwarf Stars?

It is generally assumed that metals detected in the spectra of a few cool white dwarfs cannot be of primordial origin and must be accreted from the interstellar medium. However, the observed abundances of hydrogen, which should also be accreted from the interstellar medium, are lower than expected from metal accretion. Magnetic fields are thought to be the reason for this discrepancy. We have therefore obtained circular polarization spectra of the helium-rich white dwarfs GD40 and L745-46A, which both show strong metal lines as well as hydrogen. Whereas L745-46A might have a magnetic field of about -6900 G, which is about two times the field strength of 3000G necessary to repell hydrogen at the Alfen radius, only an upper limit for the field strength of GD40 of 4000G (with 99% confidence) can be set which is far off the minimum field strength of 144000G to repell hydrogen.Comment: 4 LaTeX pages, 4 eps figures, to appear in the proceedings of the 14th European Workshop on White Dwarfs, eds. D. Koester and S. Moehler, ASP Conf. Serie

Building an infrastructure for financial stability: an overview

Financial crises ; Bank supervision ; Monetary policy