Add to ORKGThis thesis presents some problems of chance on the sum of counting numbers. It gives the probability that the sum is a perfect square, odd, even, equal to n or equal to n - 1. These probabilities were proven by means of mathematical induction.This study also gives the probability that the sum is relatively prime to n, using the Euler phi-function. The theoretical discussion is based on the article by Robert W. Prielipp entitled The Euler -Function and a Problem of Chance. A table of sums of integers from 1 to n when n = 2 to n = 12 is given. Illustrations and examples are provided. The proofs of lemmas, theorems and corollaries in the preliminary framework and the main body are presented in a very detailed manner
L'objet de cette thèse est l'étude de certaines propriétés arithmétiques et combinatoires de la fonc...
A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneousl...
AbstractThis paper begins with the statistics of the decimal digits of n/d with (n,d)∈N2 randomly ch...
This thesis presents some problems of chance on the sum of counting numbers. It gives the probabilit...
Euler's $\phi$ function, which counts the number of positive integers relative prime to and smaller ...
The problem of representing odd integers as the sum of a prime and a power of two is investigated us...
We study weighted versions of Dirichlet's theorem on the probability that two integers, taken at ran...
AbstractLet Pk(n) denote the probability that k positive integers, chosen at random from {1, 2,…, n}...
This paper begins with the statistics of the decimal digits of $n/d$ with n, d positive integers ran...
Understanding probability is very important, not only within the fields of mathematics and computer ...
We review some probabilistic properties of the sum-of-digits function of random integers. New asympt...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
This work aims at the study of arithmetic functions and the study of elementary theorems about the ...
AbstractWe study weighted versions of Dirichlet's theorem on the probability that two integers, take...
This paper begins with the statistics of the decimal digits of n/d with n, d randomly chosen. Starti...
L'objet de cette thèse est l'étude de certaines propriétés arithmétiques et combinatoires de la fonc...
A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneousl...
AbstractThis paper begins with the statistics of the decimal digits of n/d with (n,d)∈N2 randomly ch...
This thesis presents some problems of chance on the sum of counting numbers. It gives the probabilit...
Euler's $\phi$ function, which counts the number of positive integers relative prime to and smaller ...
The problem of representing odd integers as the sum of a prime and a power of two is investigated us...
We study weighted versions of Dirichlet's theorem on the probability that two integers, taken at ran...
AbstractLet Pk(n) denote the probability that k positive integers, chosen at random from {1, 2,…, n}...
This paper begins with the statistics of the decimal digits of $n/d$ with n, d positive integers ran...
Understanding probability is very important, not only within the fields of mathematics and computer ...
We review some probabilistic properties of the sum-of-digits function of random integers. New asympt...
The divisor function $\tau(n)$ counts the number of positive divisors of an integer n. We are concer...
This work aims at the study of arithmetic functions and the study of elementary theorems about the ...
AbstractWe study weighted versions of Dirichlet's theorem on the probability that two integers, take...
This paper begins with the statistics of the decimal digits of n/d with n, d randomly chosen. Starti...
L'objet de cette thèse est l'étude de certaines propriétés arithmétiques et combinatoires de la fonc...
A heuristic in analytic number theory stipulates that sets of positive integers cannot simultaneousl...
AbstractThis paper begins with the statistics of the decimal digits of n/d with (n,d)∈N2 randomly ch...