The problem of whether there exists a composite n for which φ(n) \ n — 1 (φ is Euler's function) was first posed by D. H. Lehmer in 1932 and still remains unsolved. In this paper we prove that the number of such n not exceeding x is O(x(logx)). We also prove that any such n with precisely K distinct prime factors is necessarily less than K. There are appropriate generalizations of these results...

zno nanorods and nanoparticles have been easily prepared via the decomposition of two simple schiff base zinc (ii) complexes, namely (n,n'–disalicylalethylenediamine)zince(ii) and (n,n'–disalicylalphenylenediamine)zince(ii) under microwave irradiation. the decomposition products of the complexes were characterized by ft-ir, xrd, sem, edx and uv-visible spectroscopy.  ft-ir, xrd and edx results ...

The mononuclear Ni(II) amide, [Ni(C(12)H(21)N(2)Si)(2)], has the Ni(II) atom N,N'-chelated by the N-silylated anilinide ligands. The ligands are arranged cis to each other and obey the C(2)-symmetry operation. The two ends of the N-Si-N chelating unit exhibit different affinities for the metal atom: the Ni-N(anilinide) bond length is 1.913 (3) Å and Ni-N(amine) is 2.187 (3) Å. The four-coordina...