A note on the products (1(mu)+1)(2(mu)+1) ... (n(mu)+1)

Let Omega(mu)(n) = (1(mu) + 1)(2(mu) + 1) ... (n(mu) + 1) where mu >= 2 is an integer. We prove that Omega(3)(n) is never squarefull, and in particular never a square, using arguments similar to those in J. Cilleruelo (2008) [2], where it is proven that Omega(2)(n) is not a square for n not equal 3. In T. Amdeberhan et al (2008) [1], among many other results, it is claimed that Omega(mu)(n) is not a square if mu is an odd prime and n > 12. However, we have found a gap in the proof of this statement, which we illustrate by giving counterexamples.


Tight contact structures on hyperbolic three-manifolds
Arıkan, Mehmet Fırat (Elsevier BV, 2017-11-01)
Let Sigma(g) denote a closed orientable surface of genus g >= 2. We consider a certain infinite family of Sigma(g)-bundles over circle whose monodromies are taken from some collection of pseudo-Anosov diffeomorphisms. We show the existence of tight contact structure on every closed 3-manifold obtained via rational r-surgery along a section of any member of the family whenever r not equal 2g - 1. Combining with Thurston's hyperbolic Dehn surgery theorem, we obtain infinitely many hyperbolic closed 3-manifold...
Joint linear complexity of arbitrary multisequences consisting of linear recurring sequences
Fu, Fang-Wei; Niederreiter, Harald; Özbudak, Ferruh (Elsevier BV, 2009-08-01)
Let g(1),..., g(s) is an element of F-q[x] be arbitrary nonconstant monic polynomials. Let M(g(1),..., g(s)) denote the set of s-fold multisequences (sigma(1),...,sigma(s)) such that sigma(i) is a linear recurring sequence over F-q with characteristic polynomial g(i) for each 1 <= i <= s. Recently, we obtained in some special cases (for instance when gl,..., gs are pairwise coprime or when g(1) = ... = g(s)) the expectation and the variance of the joint linear complexity of random multisequences that are un...
Lambda(b) -> Lambda l(+)l(-) decay in universal extra dimensions
Alıyev, Tahmasıb; Savcı, Mustafa (Springer Science and Business Media LLC, 2007-03-01)
We study the exclusive Lambda(b) ->Lambda l(+)l(-)(l = mu,Gamma) decay in the Appelquist, Chang, Dobrescu model with a single universal extra dimension. We investigate the sensitivity of the branching ratio, lepton polarization and forward-backward asymmetry A(FB) to the compactification parameter 1/R. We obtain the result that the branching ratio for the Lambda(b) -> Lambda l(+)l(-) (l = mu, T) decay changes about 25% compared to the SM value when 1/R = 250 GeV, and the zero position of the forward-backwar...
Substitution kinetics of Cr(CO)(5)(eta(2)-Z-cyclooctene) with tetracyanoethylene
Kozanoglu, F; Saldamli, S; Özkar, Saim (Elsevier BV, 2002-09-16)
The weakly bound Z-cyclooctene (zco) ligand in Cr(CO)(5)(eta(2)-zco) is replaced by tetracyanoethylene (tcne) at an observable rate in the temperature range between - 5 and + 10 degreesC yielding the complex Cr(CO)(5)(eta(2)-tcne) as the final product The kinetics of this substitution reaction was studied in toluene solution containing 5% by volume zco by quantitative FTIR spectroscopy The substitution reaction obeys a pseudo-first order kinetics with respect to the concentration of the starting complex. Th...
Planarity of products of two linearized polynomials
KYUREGHYAN, Gohar; Özbudak, Ferruh (2012-11-01)
Let L-1(x) and L-2(x) be linearized polynomials over F-qn. We give conditions when the product L-1(x) . L-2(x) defines a planar mapping on F-qn. For a polynomial L over F-qn, let M(L) = {alpha is an element of F-qn: L(x) + alpha . x is bijective on F-qn}. We show that the planarity of the product L-1(x) . L-2(x) is linked with the set M(L) of a suitable linearized polynomial L. We use this relation to describe families of such planar mappings as well as to obtain nonexistence results. (c) 2012 Elsevier Inc....
Citation Formats
E. Guerel and A. U. Ö. Kişisel, “A note on the products (1(mu)+1)(2(mu)+1) ... (n(mu)+1),” JOURNAL OF NUMBER THEORY, pp. 187–191, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48653.