A190356 -id:A190356 - cp's OEIS frontend

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

Jean-François Alcover, May 13 2011

sign

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

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

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 ...

Cf. A020898, A060838, A190356, A190581.

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

A190581 Value of z in the Diophantine equation x^3 + y^3 = n*z^3 (with x>0 and minimal and x >= y and y != 0).

Original entry on oeis.org

1, 21, 1, 1, 39, 3, 294, 7, 1, 7, 9954, 1, 1, 57, 42, 582, 182, 1, 1, 129, 2, 3, 6111, 197028, 217, 7083, 1, 3, 1, 1, 1323, 620505, 3318, 13, 43, 3606, 1302, 3, 111, 330498, 3, 216266610, 13, 273, 1, 5733, 590736058375050, 3, 1, 117, 1014, 25767, 19, 37, 1878, 1029364, 1, 37045412880, 1, 1, 1, 11285694

Offset: 1

Jean-François Alcover, May 13 2011

nonn

A190356(n)^3 + y^3 = A020898(n)*a(n)^3. Unknown y corresponds to sequence A190580.

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

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

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 ...

Cf. A020898, A060838, A190356, A190580

a[n_] := z /. ToRules[ Reduce[ z > 0 && A190356[[n]]^3 + A190580[[n]]^3 == A020898[[n]]*z^3, z, Integers]]; Table[a[n] , {n, 1, 62}]

cp's OEIS Frontend

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).

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