タクシー数
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脚注^ Silverman (1983)
^ Dickson (1919, p. 552)
^ Hardy & Wright (2008, Theorem 235)
^ Quotations by Hardy - ウェイバックマシン（2017年8月29日アーカイブ分）
^ Ken Ono and Sarah Trebat-Leder (2016, 2017)
^ Numbers Count column of Personal Computer World, page 610, Feb 1995
^ "The Fifth Taxicab Number is 48988659276962496" by David W. Wilson
^ ⇒NMBRTHRY Archives - March 2008 (#10) "The sixth taxicab number is 24153319581254312065344" by Uwe Hollerbach
^ C. S. Calude, E. Calude and M. J. Dinneen: What is the value of Taxicab(6)?, Journal of Universal Computer Science, Vol. 9 (2003), p. 1196-1203
^ ⇒Tables of best known results (in May 2007) on Taxicab and Cabtaxi numbers
^ ⇒New Upper Bounds for Taxicab and Cabtaxi numbers
^ Silverman (1982)
参考文献
Hardy, G.H.; Wright, E.M. (2008) [1938]. An Introduction to the Theory of Numbers. Revised by D.R. Heath-Brown and J.H. Silverman. Foreword by Andrew Wiles. (6th ed.). Oxford: Oxford University Press. .mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation.cs-ja1 q,.mw-parser-output .citation.cs-ja2 q{quotes:"「""」""『""』"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:#d33}.mw-parser-output .cs1-visible-error{color:#d33}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}ISBN 978-0-19-921986-5. Zbl 1159.11001
Dickson, Lernard Eugene (1919). History of the theory of numbers, vol. II, Diophantine Analysis. Carnegie Institute of Washington. https://archive.org/details/historyoftheoryo02dickuoft
J. Leech, Some Solutions of Diophantine Equations, Proc. Cambridge Phil. Soc. 53, 778-780, 1957.
Ono, Ken; Trebat-Leder, Sarah (2016). “The 1729 K3 surface”. Res. Number Theory 2: No. 26. doi:10.1007/s40993-016-0058-2.
Ono, Ken; Trebat-Leder, Sarah (2017). “Erratum to: The 1729 K3 surface”. Res. Number Theory 3: No. 12. doi:10.1007/s40993-017-0076-8.
E. Rosenstiel, J. A. Dardis and C. R. Rosenstiel, The four least solutions in distinct positive integers of the Diophantine equation s = x3 + y3 = z3 + w3 = u3 + v3 = m3 + n3, Bull. Inst. Math. Appl., 27(1991) 155-157; MR 92i:11134, ⇒online. 「Personal Computer World」1989年11月号も参照せよ。
David W. Wilson, The Fifth Taxicab Number is 48988659276962496, Journal of Integer Sequences, Vol. 2 (1999), ⇒online. (ウィルソンはこれを著した際、1994年にJ・A・ダーディスがTa(5)を発見していたことを認識していなかった）
D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d), Mathematics of Computation 70, 233 (2000), 389–394.
C. S. Calude, E. Calude and M. J. Dinneen: What is the value of Taxicab(6)?, Journal of Universal Computer Science, Vol. 9 (2003), p. 1196–1203
Silverman, Joseph H. (1983). “Integer points on curves of genus 1”. J. London Math. Soc. (2) 28: 1-7. doi:10.1112/jlms/s2-28.1.1. MR0703458.
Silverman, Joseph H. (1982). “Integer points and the rank of Thue elliptic curves”. Invent. Math. 66: 395-404. doi:10.1007/BF01389220. MR0662599.
関連項目
キャブタクシー数
一般化タクシー数
外部リンク
Weisstein, Eric W. "Taxicab Number". mathworld.wolfram.com (英語).
⇒A 2002 post to the Number Theory mailing list by Randall L. Rathbun
⇒Taxicab and other maths at Euler
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