{"id":{"repo_id":"wfu","oai_identifier":"oai:wakespace.lib.wfu.edu:10339/37313"},"canonical_url":"https://search.dev.ndltd.org/etd/wfu/oai:wakespace.lib.wfu.edu:10339/37313","repository":{"repo_id":"wfu","name":"Wake Forest University","base_url":"https://wakespace.lib.wfu.edu/oai/request"},"display":{"title":"The Z-densities of the Fibonacci Sequence","abstract":"Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n\" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m\" to be Z(m) is the limit of x to infinity of M(m,x) divided by pi(x). The conjecture gives a formula for Z(m) for all positive m. We will prove the conjecture of Bruckman and Anderson.","abstract_html":"Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m" to be Z(m) is the limit of x to infinity of M(m,x) divided by pi(x). The conjecture gives a formula for Z(m) for all positive m. We will prove the conjecture of Bruckman and Anderson.","abstract_has_math":false,"creators":["Cubre, Paul"],"institution":"Wake Forest University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-27T22:01:27Z","subjects":["Arithmetic Dynamics"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10339/37313","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Cubre, Paul"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2012-06-12T08:36:06Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2012-06-12T08:36:06Z"]},{"key":"dc:date.issued","label":"Date","values":["2012"]},{"key":"dc:publisher","label":"Institution","values":["Wake Forest University"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Arithmetic Dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10339/37313"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n\" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m\" to be Z(m) is the limit of x to infinity of M(m,x) divided by pi(x). The conjecture gives a formula for Z(m) for all positive m. We will prove the conjecture of Bruckman and Anderson."]},{"key":"dc:title","label":"Title","values":["The Z-densities of the Fibonacci Sequence"]}]}],"canonical_facts":{"dc:creator":["Cubre, Paul"],"dc:date.accessioned":["2012-06-12T08:36:06Z"],"dc:date.available":["2012-06-12T08:36:06Z"],"dc:date.issued":["2012"],"dc:description.abstract":["Paul S. Bruckman and Peter G. Anderson made a conjecture about the Z-densities of the Fibonacci sequence, F(n), based on computational results. For a prime p, Z(p) is the ``Fibonacci entry-point of n\" or the smallest positive integer n such that p divides F(n), M(m,x) is the number of primes p is less than x such that m divides Z(p), and pi(x) is the number of primes less than x. We may define the ``Z-density of m\" to be Z(m) is the limit of x to infinity of M(m,x) divided by pi(x). The conjecture gives a formula for Z(m) for all positive m. We will prove the conjecture of Bruckman and Anderson."],"dc:identifier.uri":["http://hdl.handle.net/10339/37313"],"dc:language.iso":["en"],"dc:publisher":["Wake Forest University"],"dc:subject":["Arithmetic Dynamics"],"dc:title":["The Z-densities of the Fibonacci Sequence"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T22:01:27Z"}