A060387 Numbers k such that x^4 + y^4 = k * z^4 is solvable in nonzero integers x,y,z.

2, 17, 32, 82, 97, 162, 257, 272, 337, 512, 626, 641, 706, 881, 1250, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2592, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 4802, 5392, 5906

Offset

1,1

Comments

Numbers k such that k = x^4 + y^4 has a solution in positive rationals x, y.

Links

Table of n, a(n) for n=1..35.

A. Bremner and P. Morton, A new characterization of the integer 5906, Manuscripta Math. 44 (1983) 187-229; Math. Rev. 84i:10016.

Steven R. Finch, On a generalized Fermat-Wiles equation [broken link]

Steven R. Finch, On a Generalized Fermat-Wiles Equation [From the Wayback Machine]

Eric Weisstein's World of Mathematics, Biquadratic Number

Mathematica

r[n_, z_] := Reduce[0 < x <= y && x^4 + y^4 == n*z^4, {x, y}, Integers]; zm[_] = 1; zm[5906] = 17; ok[n_] := (tf = False; Do[ If[ r[n, z] =!= False, tf = True; Break[]], {z, 1, zm[n]}]; tf); A060387 = Reap[ Do[ If[ ok[n], Print[n]; Sow[n]], {n, 1, 5906}]][[2, 1]](* Jean-François Alcover, Mar 09 2012 *)

Crossrefs

5906 is the first term not in A003336. Cf. A020897.

Cf. A111152, A209431.

Sequence in context: A141068 A162622 A078164 * A003336 A344187 A212740

Adjacent sequences: A060384 A060385 A060386 * A060388 A060389 A060390

Keyword

nonn,nice,more

Author

Michel ten Voorde, Apr 04 2001

Status

approved