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Classes of Equations of the Type y2 = x3 + k Having No Rational Solutions
Published online by Cambridge University Press: 22 January 2016
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The equation y2 = x3 + k, k an integer, has been discussed by many authors. Mordell [1] has found many classes of k values for which the equation has no integral solutions. Fueter [2], Mordell [3] and Chang [4] have found classes of k values for which the equation has no rational solutions. The following two theorems exhibit two more sets of conditions which give rise to classes of k values for which the corresponding equations have no rational solutions.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1966