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A060387
Numbers k such that x^4 + y^4 = k * z^4 is solvable in nonzero integers x,y,z.
4
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
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.
Sequence in context: A141068 A162622 A078164 * A003336 A344187 A212740
KEYWORD
nonn,nice,more
AUTHOR
Michel ten Voorde, Apr 04 2001
STATUS
approved