{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T20:19:35Z","timestamp":1777407575799,"version":"3.51.4"},"reference-count":8,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,6,1]],"date-time":"2025-06-01T00:00:00Z","timestamp":1748736000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T00:00:00Z","timestamp":1748908800000},"content-version":"vor","delay-in-days":2,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/100016977","name":"Kogakuin University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100016977","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Game Theory"],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00182-025-00948-0","type":"journal-article","created":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T04:23:05Z","timestamp":1748924585000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Odd case of 2-pile divisor Nim"],"prefix":"10.1007","volume":"54","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-1898-2515","authenticated-orcid":false,"given":"Takayuki","family":"Morisawa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,3]]},"reference":[{"key":"948_CR1","doi-asserted-by":"publisher","first-page":"35","DOI":"10.2307\/1967631","volume":"3","author":"CL Bouton","year":"1901","unstructured":"Bouton CL (1901) Nim, a game with a complete mathematical theory. Ann Math 3:35\u201339","journal-title":"Ann Math"},{"key":"948_CR2","doi-asserted-by":"publisher","first-page":"209","DOI":"10.47443\/dml.2023.154","volume":"12","author":"P Ellis","year":"2023","unstructured":"Ellis P, Shi J, Thanatipanonda TA, Tu A (2023) Two games on arithmetic functions: SALIQUANT and NONTOTIENT. Discr Math Lett 12:209\u2013216","journal-title":"Discr Math Lett"},{"key":"948_CR3","first-page":"6","volume":"2","author":"PM Grundy","year":"1939","unstructured":"Grundy PM (1939) Mathematics and games. Eureka 2:6\u20138","journal-title":"Eureka"},{"key":"948_CR4","doi-asserted-by":"crossref","unstructured":"Iannucci DE, Larsson U (2021) Game values of arithmetic functions. Integers 21B memorial volume for Berlekamp, Conway and Guy, A14","DOI":"10.1515\/9783110755411-014"},{"issue":"1","key":"948_CR5","first-page":"84","volume":"41","author":"I Makino","year":"2023","unstructured":"Makino I (2023) On grundy number of a [CDATA[2]]$$2$$-pile Nim. Waseda J Math Educ 41(1):84\u201391","journal-title":"Waseda J Math Educ"},{"issue":"1","key":"948_CR6","first-page":"31","volume":"42","author":"I Makino","year":"2024","unstructured":"Makino I, Morisawa T (2024) On periodicity of $$2$$[CDATA[2]]-pile divisor Nim. Waseda J Math Educ 42(1):31\u201341","journal-title":"Waseda J Math Educ"},{"issue":"1","key":"948_CR7","first-page":"42","volume":"42","author":"T Morisawa","year":"2024","unstructured":"Morisawa T (2024) Winning strategy in $$2$$[CDATA[2]]-pile divisor Nim. Waseda J Math Educ 42(1):42\u201347","journal-title":"Waseda J Math Educ"},{"key":"948_CR8","first-page":"438","volume":"41","author":"RP Sprague","year":"1935","unstructured":"Sprague RP (1935) \u00dcber mathematische Kampfspiele. Tohoku Math J 41:438\u2013444","journal-title":"Tohoku Math J"}],"container-title":["International Journal of Game Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-025-00948-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00182-025-00948-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00182-025-00948-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T10:29:54Z","timestamp":1757154594000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00182-025-00948-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["948"],"URL":"https:\/\/doi.org\/10.1007\/s00182-025-00948-0","relation":{},"ISSN":["0020-7276","1432-1270"],"issn-type":[{"value":"0020-7276","type":"print"},{"value":"1432-1270","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6]]},"assertion":[{"value":"14 May 2025","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 June 2025","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"21"}}