{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:36:15Z","timestamp":1776800175332,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,6,26]],"date-time":"2016-06-26T00:00:00Z","timestamp":1466899200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We consider the system of nonlinear almost polynomial equations without power gaps or with even power gaps. The method is to reduce the given system to finding the roots of univariate functions, some of which are polynomials. For the system with even power gaps the obtained equalities are the analogs of Newton\u2019s identities. These equalities express the connection between elementary symmetric functions and odd power sums.<\/p>","DOI":"10.1090\/mcom\/2994","type":"journal-article","created":{"date-parts":[[2015,6,26]],"date-time":"2015-06-26T08:45:03Z","timestamp":1435308303000},"page":"717-736","source":"Crossref","is-referenced-by-count":1,"title":["Almost power sum systems"],"prefix":"10.1090","volume":"85","author":[{"given":"V.","family":"Korobov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A.","family":"Bugaevskaya","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,6,26]]},"reference":[{"key":"1","unstructured":"U. J. J. Le Verrier, Sur les variations s\u00e9culaires des \u00e9l\u00e9ments elliptiques des sept plan\u00e8tes principales, J. Math. Pures Appl., S\u00e9r. 1, T. 5 (1840), pp. 220\u2013254."},{"key":"2","unstructured":"P. L. Chebyshev, Sur les quadratures, J. Math. Pures Appl., S\u00e9r. 2, Vol. 19 (1874), pp. 19\u201334."},{"key":"3","unstructured":"S. N. Bernstein, Sur la formule de quadrature approche de Tchebycheff, C. R. Math. Acad. Sci. Paris, 203 (1936), pp. 1305\u20131306."},{"key":"4","doi-asserted-by":"crossref","unstructured":"F. G. Mehler, Bemerkungen zur Theorie der mechanischen Quadraturen, J. Reine Angew. Math., Vol. 1864 (1864), Issue 63 (Jan 1, 1864) (1864), pp. 152\u2013157.","DOI":"10.1515\/crll.1864.63.152"},{"key":"5","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1307\/mmj\/1028999599","article-title":"A class of weight functions that admit Tchebycheff quadrature","volume":"13","author":"Ullman, J. L.","year":"1966","journal-title":"Michigan Math. 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