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Home > Art, Film & Photography > Disproved Conjectures: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec
Disproved Conjectures: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec

Disproved Conjectures: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec


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About the Book

Chapters: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjecture, Polya Conjecture, Schoen-Yau Conjecture, Chinese Hypothesis, Hauptvermutung, Ganea Conjecture, Von Neumann Conjecture, Ono's Inequality, Weyl-Berry Conjecture. Source: Wikipedia. Pages: 43. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem which was proposed by Leonhard Euler in 1769. It states that for all integers n and k greater than 1, if the sum of n kth powers of positive integers is itself a kth power, then n is not smaller than k. In symbols, if where and are positive integers, then . If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n = 2: if, then . The conjecture was disproven by L. J. Lander and T. R. Parkin in 1966 when they found the following counterexample for k = 5: 27 + 84 + 110 + 133 = 144. In 1986, Noam Elkies found a method to construct counterexamples for the k = 4 case. His smallest counterexample was the following: 2682440 + 15365639 + 18796760 = 20615673.A particular case of Elkies' solution can be reduced to the identity, (85v+484v313) + (68v586v+10) + (2u) = (357v204v+363)where u = 22030+28849v56158v+36941v31790v.This is an elliptic curve with one solution as v1 = 31/467. From this initial rational point, one can then compute an infinite number of vi. Substituting v1 into the identity and removing common factors gives the numerical example cited above. In 1988, Roger Frye subsequently found the smallest possible k = 4 counterexample by a direct computer search using techniques suggested by Elkies: 95800 + 217519 + 414560 = 422481.Moreover, this solution is the only one with values of the variables be...More: http: //booksllc.net/?id=9660


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Product Details
  • ISBN-13: 9781157048190
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 44
  • Spine Width: 3 mm
  • Weight: 77 gr
  • ISBN-10: 1157048196
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec
  • Width: 229 mm


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Disproved Conjectures: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec
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Disproved Conjectures: Euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk'euler's Sum of Powers Conjecture, Tait's Conjecture, Borsuk's Conjecture, Mertens Conjec

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