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).

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

Author

Jean-François Alcover, May 13 2011

Keywords

• nonn

Comments

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

Examples

			a(18) = 1  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, A190580

Programs

Mathematica

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}]