{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:43:56Z","timestamp":1760240636181,"version":"build-2065373602"},"reference-count":7,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,11]],"date-time":"2019-08-11T00:00:00Z","timestamp":1565481600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Let    V    be a finite set of positive integers with sum equal to a multiple of the integer    b   . When does    V    have a partition into    b    parts so that all parts have equal sums? We develop algorithmic constructions which yield positive, albeit incomplete, answers for the following classes of set    V   , where    n    is a given positive integer: (1) an initial interval      {  a \u2208  \u2124 +  : a \u2264 n  }     ; (2) an initial interval of primes      {  p \u2208 \u2119 : p \u2264 n  }     , where    \u2119    is the set of primes; (3) a divisor set      {  d \u2208  \u2124 +  : d | n  }     ; (4) an aliquot set      {  d \u2208  \u2124 +  : d | n , \u00a0 d &lt; n  }     . Open general questions and conjectures are included for each of these classes.<\/jats:p>","DOI":"10.3390\/a12080164","type":"journal-article","created":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T06:38:02Z","timestamp":1565591882000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Equisum Partitions of Sets of Positive Integers"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2218-394X","authenticated-orcid":false,"given":"Roger B.","family":"Eggleton","sequence":"first","affiliation":[{"name":"School of Mathematical and Physical Sciences, University of Newcastle, Newcastle 2308, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,11]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., and Wright, E.M. (1979). An Introduction to the Theory of Numbers, Clarendon Press. [5th ed.]. reprinted by Clarendon Press: Oxford, UK, 1988."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Nathanson, M.B. (1996). Additive Number Theory, Springer.","DOI":"10.1007\/978-1-4757-3845-2"},{"key":"ref_3","first-page":"212","article-title":"Beweis einer Baudetschen Vermutung","volume":"15","year":"1927","journal-title":"Nieuw Arch. Wisk."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"481","DOI":"10.4007\/annals.2008.167.481","article-title":"The primes contain arbitrarily long arithmetic progressions","volume":"167","author":"Green","year":"2008","journal-title":"Ann. Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Guy, R.K., and Chapter, C. (2004). Additive Number Theory. Unsolved Problems in Number Theory, Springer. [3rd ed.].","DOI":"10.1007\/978-0-387-26677-0"},{"key":"ref_6","unstructured":"OEIS A000396: Perfect numbers. OEIS: The On-Line Encyclopedia of Integer Sequences, Available online: https:\/\/oeis.org."},{"key":"ref_7","unstructured":"Eggleton, R.B. (2019). A geometric view of divisors and aliquot parts of integers, in preparation."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/8\/164\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:10:22Z","timestamp":1760188222000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/8\/164"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,11]]},"references-count":7,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["a12080164"],"URL":"https:\/\/doi.org\/10.3390\/a12080164","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,8,11]]}}}