There are no multiply-perfect Fibonacci numbers

Here, we show that no Fibonacci number (larger than 1) divides the sum of its divisors

Effectiveness of neem seed oil (Azadirachta indica A. Juss: Meliaceae) on Syllepte derogata Fabricius, Lepidoptera: Pyralidae

Objective: Synthetic insecticides have long been used for cotton protection,  resulting in pest resistance, toxicity and environmental pollution. Biopesticides have been suggested as alternatives to synthetic pesticides. Both field and laboratory experiments were conducted to evaluate the effectiveness of neem oil in controlling Syllepte derogata (Fabricius), a cotton phyllophagous pest.Methodology and Results: In the field trials, effect of neem oil was compared to that of conventional insecticides; while in the laboratory direct larval immersion and leaf dip method using EMA SUPER 56DC and neem oil were tested. Decrease in damage by S. derogata for about 63 and 86% was recorded with neem oil and synthetic insecticides. In the laboratory, the mortality of S. derogata after 24 hours exposure to neem oil and Ema Super was significantly higher (2.5 to 100%) than that of the control. The mortality of larvae of S. derogata was positively correlated with the concentration of neem oil and exposure time. Lethal Concentration (LC50) after 24 hours exposure of larvae was respectively 4.03 104 ml/l and 51.13 ml/l forleaf dipping method and larval immersion.Conclusion and application of results: Overall, these results showed the efficacy of neem oil in controlling S. derogata, as a biopesticide. This oil could also  constitute a successful alternative to synthetic pesticides. However, the  effectiveness of neem oil appeared to be weakened by the rapid degradation of the active substances, azadirachtin in particular. Indeed, azadirachtin, the main active ingredient of neem is photo and heat labile. It easily degrades under high solar radiations and high temperatures, hence the need for stabilization.Keywords: Phyllophagous pest, integrated pest management, leaf-dipping method, larval immersion, Lethal Concentration

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

Etude cristallochimique des muscovites de Pagala-Togo

(J. de la Recherche Scientifique de l'Université de Lomé, 2000, 4(2): 251-257

Les chapeaux de fer du Togo: micromorphologie et genèse des figures de remplacement

(Journal de la Recherche Scientifique de l'Université de Lomé: 2001 5(1): 137-144

Can a Lucas number be a sum of three repdigits?

summary:We give the answer to the question in the title by proving that \begin{equation*} L_{18} = 5778 = 5555 + 222 + 1 \end{equation*} is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits

Triangular repblocks

In this paper, we prove a finiteness theorem concerning repblocks of two digits in base 10, which are represented by a fixed quadratic polynomial. We also show that the only repblocks of two digits that are triangular numbers are 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 5050, 5151