On derivational arithmetics - Solution for the proposed problems in “How to differentiate a number” by Victor Ufnarovski?
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Specialised Paper - Mathematics On the arithmetic derivative Solution for the proposed problems in “How to differentiate a number” by Victor Ufnarovski Contents 1 Preliminary remarks and definitions 2 The problems 3 Proofs 4 Defining the operators 5 General properties 6 Set memberships 1 Preliminary remarks and definitions The aim of this paper is to solve some problems proposed by Victor Ufnarovski in his work “How to differentiate a number”. The problems are in some way concerned with the twin primes problem and the Goldbach conjecture. The arithmetic derivative n’ of a natural number n is defined the following way: 1. n’=1 for any prime n 2. (ab)’=a’b+ab’ for any pair of natural numbers (a,n) 3. 1’=0’=0 The solutions proposed by this paper may build on a conjecture I introduce inhere: Conjecture 1. Call the set of numbers of…[show more]