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The Choix de Bruxelles operation replaces a positive integer n by any of the numbers that can be obtained by halving or doubling a substring of the decimal representation of n. For example, 16 can become any of 16, 26, 13, 112, 8, or 32. We investigate the properties of this interesting operation and its iterates.
Observation of the workings of productive organizations shows that the characteristics of a trade, backed by nature given to a technological environment, determine the productive combination implemented by the decision maker, and the structure of the
Given a negative $D>-(log X)^{log 2-delta}$, we give a new upper bound on the number of square free integers $<X$ which are represented by some but not all forms of the genus of a primitive positive definite binary quadratic form $f$ of discriminant
We discuss $Q(n)$, the number of ways a given integer $n$ may be written as a sum of distinct primes, and study its asymptotic form $Q_{as}(n)$ valid in the limit $ntoinfty$. We obtain $Q_{as}(n)$ by Laplace inverting the fermionic partition function
For k>=3 let A subset [1,N] be a set not containing a solution to a_1 x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that there is an epsilon>0 depending on the coefficients of the equation such that every such A has O(N^{1
Hecke studies the distribution of fractional parts of quadratic irrationals with Fourier expansion of Dirichlet series. This method is generalized by Behnke and Ash-Friedberg, to study the distribution of the number of totally positive integers of gi