{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T07:44:25Z","timestamp":1775461465279,"version":"3.50.1"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2000,12]]},"abstract":"<jats:p> Let G be a finite group. A Corollary of a result of Gerstenhaber and Rothaus [3] states that all equations in one variable over G with exponent sum nonzero are solvable over G. Lyndon [6] studied equations in one variable with exponent sum zero over Z<jats:sub>m<\/jats:sub>. He showed that there was a relatively simple equation with no solution over Z<jats:sub>2<\/jats:sub>. In this paper we will initiate a study of equations with exponent sum zero over Z<jats:sub>2<\/jats:sub>. In particular we will show whether or not certain equations, which are generalizations of the equation studied by Lyndon, have solutions over Z<jats:sub>2<\/jats:sub>. We are grateful to the referee whose suggestion for the case when p&lt;0&lt;q both simplified and generalized our original result. This paper constitutes part of the theses of the first and third named authors. <\/jats:p>","DOI":"10.1142\/s0218196700000339","type":"journal-article","created":{"date-parts":[[2003,4,22]],"date-time":"2003-04-22T07:48:21Z","timestamp":1050997701000},"page":"709-723","source":"Crossref","is-referenced-by-count":3,"title":["ON THE SOLUTION OF CERTAIN EQUATIONS WITH EXPONENT SUM 0 OVER  Z<sub>2<\/sub>"],"prefix":"10.1142","volume":"10","author":[{"given":"V.","family":"FERLINI","sequence":"first","affiliation":[{"name":"Keene State, SUNY Albany, SUNY Albany, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"GOLDSTEIN","sequence":"additional","affiliation":[{"name":"Keene State, SUNY Albany, SUNY Albany, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"SALPUKAS","sequence":"additional","affiliation":[{"name":"Keene State, SUNY Albany, SUNY Albany, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500019283"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.48.9.1531"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500028108"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1962-10868-4"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/BF02584882"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-18.1.4"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196700000339","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:22:52Z","timestamp":1565133772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196700000339"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,12]]},"references-count":6,"aliases":["10.1016\/s0218-1967(00)00033-9"],"journal-issue":{"issue":"06","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2000,12]]}},"alternative-id":["10.1142\/S0218196700000339"],"URL":"https:\/\/doi.org\/10.1142\/s0218196700000339","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,12]]}}}