Matches in SemOpenAlex for { <https://semopenalex.org/work/W791386007> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W791386007 abstract "As a generalization of the equation 0(x) + 0(&) = 0(x + /t), 0-partitions and reduced 0partitions and reduced 0 -partitions of positive integers were considered by Patricia Jones [1]. That is., n = ax + —-at is a 0 -partition if i > 1 and where 0 is Euler's totient function. Furthermore, a 0 -partition is reduced if each of its summands is simple, where a simple number is known as 1 or a product of the first primes. In [1] the author conjectured that every nonsimple number has exactly one reduced 0partition. Here, we show that the conjecture is false. In fact, we will see that the positive integers satisfying the conjecture are quite rare. The main purpose of this paper is to give a complete characterization of positive integers that have exactly one reduced 0 -partition. Throughout the paper, let/? and q denote distinct primes, especially, pi denote the I prime, and AQ = 1, Al; = Ylp<p P be the I simple number. It is shown in [1] that every simple number has no 0 -partitions and every nonsimple number has a 0 -partition as follows:" @default.
- W791386007 created "2016-06-24" @default.
- W791386007 creator A5042241049 @default.
- W791386007 date "1993-01-01" @default.
- W791386007 modified "2023-09-23" @default.
- W791386007 title "REDUCED ^PARTITIONS OF POSITIVE INTEGERS*" @default.
- W791386007 hasPublicationYear "1993" @default.
- W791386007 type Work @default.
- W791386007 sameAs 791386007 @default.
- W791386007 citedByCount "0" @default.
- W791386007 crossrefType "journal-article" @default.
- W791386007 hasAuthorship W791386007A5042241049 @default.
- W791386007 hasConcept C111472728 @default.
- W791386007 hasConcept C114614502 @default.
- W791386007 hasConcept C118615104 @default.
- W791386007 hasConcept C134306372 @default.
- W791386007 hasConcept C138885662 @default.
- W791386007 hasConcept C198944804 @default.
- W791386007 hasConcept C23230895 @default.
- W791386007 hasConcept C2524010 @default.
- W791386007 hasConcept C2780586882 @default.
- W791386007 hasConcept C2780990831 @default.
- W791386007 hasConcept C33923547 @default.
- W791386007 hasConcept C42812 @default.
- W791386007 hasConcept C62884695 @default.
- W791386007 hasConcept C90673727 @default.
- W791386007 hasConceptScore W791386007C111472728 @default.
- W791386007 hasConceptScore W791386007C114614502 @default.
- W791386007 hasConceptScore W791386007C118615104 @default.
- W791386007 hasConceptScore W791386007C134306372 @default.
- W791386007 hasConceptScore W791386007C138885662 @default.
- W791386007 hasConceptScore W791386007C198944804 @default.
- W791386007 hasConceptScore W791386007C23230895 @default.
- W791386007 hasConceptScore W791386007C2524010 @default.
- W791386007 hasConceptScore W791386007C2780586882 @default.
- W791386007 hasConceptScore W791386007C2780990831 @default.
- W791386007 hasConceptScore W791386007C33923547 @default.
- W791386007 hasConceptScore W791386007C42812 @default.
- W791386007 hasConceptScore W791386007C62884695 @default.
- W791386007 hasConceptScore W791386007C90673727 @default.
- W791386007 hasLocation W7913860071 @default.
- W791386007 hasOpenAccess W791386007 @default.
- W791386007 hasPrimaryLocation W7913860071 @default.
- W791386007 hasRelatedWork W1879010168 @default.
- W791386007 hasRelatedWork W2026048562 @default.
- W791386007 hasRelatedWork W2068296851 @default.
- W791386007 hasRelatedWork W2072355979 @default.
- W791386007 hasRelatedWork W2082044044 @default.
- W791386007 hasRelatedWork W2090433386 @default.
- W791386007 hasRelatedWork W2092589595 @default.
- W791386007 hasRelatedWork W2112201978 @default.
- W791386007 hasRelatedWork W2114015444 @default.
- W791386007 hasRelatedWork W2143704683 @default.
- W791386007 hasRelatedWork W2148237358 @default.
- W791386007 hasRelatedWork W2155993241 @default.
- W791386007 hasRelatedWork W2185446462 @default.
- W791386007 hasRelatedWork W2208731040 @default.
- W791386007 hasRelatedWork W2350698776 @default.
- W791386007 hasRelatedWork W2356420504 @default.
- W791386007 hasRelatedWork W2556340225 @default.
- W791386007 hasRelatedWork W2737727897 @default.
- W791386007 hasRelatedWork W2964148324 @default.
- W791386007 hasRelatedWork W3028574858 @default.
- W791386007 isParatext "false" @default.
- W791386007 isRetracted "false" @default.
- W791386007 magId "791386007" @default.
- W791386007 workType "article" @default.