A190580 Value of y in the Diophantine equation x^3 + y^3 = n*z^3 (with x>0 and minimal and x >= y and y != 0).

1, 17, -1, 1, 19, 2, 397, -1, -2, 1, 17299, -1, 1, 107, -65, 523, -359, 2, -3, -71, 1, -2, -11267, 62641, -1819, -14653, -4, 7, -1, 1, 1208, -472663, -10441, 17, -126, -11951, 53, -4, 323, -2404889, 5, -907929611, 36, -431, 3, -3547, -15616184186396177, -5, -3, -349, 3527, -140131, 17, -71, -901, -2741617, -2, 10183412861, -1, 1, -6, 33728183

Offset: 1

Author

Jean-François Alcover, May 13 2011

Keywords

• sign

Comments

A190356(n)^3 + a(n)^3 = A020898(n)*z^3. Unknown z corresponds to sequence A190581.

The 4 sequences A020898 [i.e. n], A190356 [i.e. x], A190580 [i.e. y] and A190581 [i.e. z] satisfy the equation A190356^3 + A190580^3 = A020898 * A190581^3

Examples

			a(18) = 2  because  A020898(18) = 35 and 3^3 + 2^3 = 35*1^3.
		

Links

• Steven R. Finch, On a Generalized Fermat-Wiles Equation [broken link]
• Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]
• Nakao Hisayasu, Rational Points on Elliptic Curves: x^3+y^3=n (nna2.html up to nna22.html)
• Hisanori Mishima, Solutions of Diophantine equation x^3+y^3=A.z^3 ...

Crossrefs

Cf. A020898, A060838, A190356, A190581.

Programs

Mathematica

Table[ y /. First[ Solve[ A190356[[n]]^3 + y^3 == A020898[[n]] * A190581[[n]]^3 ] ], {n, 62}] (* Jean-François Alcover, Jan 04 2012 *)