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Many of these values are derived from the essentially trivial solution {x,y,z} = {(a + b)*b*(3*a^2 + 3*a*b + b^2), a*b*(3*a^2 + 3*a*b + b^2), b*(3*a^2 + 3*a*b + b^2)}. This solution follows from the fact that (a+b)^3-a^3 = b*(3*a^2 + 3*a*b + b^2) and that multiplying this equation by [b*(3*a^2 + 3*a*b + b^2)]^3 gives a solution to y^3 - x^3 = z^4. - _James McLaughlin, Mc Laughlin_, Jan 27 2007
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Many of these values are derived from the essentially trivial solution {x,y,z} = {(a + b)*b*(3*a^2 + 3*a*b + b^2), a*b*(3*a^2 + 3*a*b + b^2), b*(3*a^2 + 3*a*b + b^2)}. This solution follows from the fact that (a+b)^3-a^3 = b*(3*a^2 + 3*a*b + b^2) and that multiplying this equation by [b*(3*a^2 + 3*a*b + b^2)]^3 gives a solution to y^3 - x^3 = z^4. - James McLaughlin, Jan 27 2007
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F. Beukers, The Diophantine equation Ax^p+By^q=Cz^r, Duke Math. J. 91 (1998), 61-88.
F. Beukers, <a href="http://dx.doi.org/10.1215/S0012-7094-98-09105-0">The Diophantine equation Ax^p+By^q=Cz^r</a>, Duke Math. J. 91 (1998), 61-88.
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