A096739 Numbers k such that k^4 can be written as a sum of four distinct positive 4th powers.

353, 651, 706, 1059, 1302, 1412, 1765, 1953, 2118, 2471, 2487, 2501, 2604, 2824, 2829, 3177, 3255, 3530, 3723, 3883, 3906, 3973, 4236, 4267, 4333, 4449, 4557, 4589, 4942, 4949, 4974, 5002, 5208, 5281, 5295, 5463, 5491, 5543, 5648, 5658, 5729, 5859

Offset: 1

Author

Lekraj Beedassy, May 30 2002

Keywords

• nonn

Comments

From David Wasserman, Nov 16 2007: (Start)

Every multiple of a term is a term.

Is this sequence the same as A003294? (End)

Examples

			Example solutions:
   353^4 =   30^4 +  120^4 +  272^4 +  315^4;
   706^4 =   60^4 +  240^4 +  544^4 +  630^4;
  1059^4 =   90^4 +  360^4 +  816^4 +  945^4;
  1302^4 =  480^4 +  680^4 +  860^4 + 1198^4;
  1412^4 =  120^4 +  480^4 + 1088^4 + 1260^4;
  3723^4 = 2270^4 + 2345^4 + 2460^4 + 3152^4.
		

References

• D. Wells, Curious and interesting numbers, Penguin Books, p. 139.

Links

• K. Rose and S. Brudno, More about four biquadrates equal one biquadrate, Math. Comp., 27 (1973), 491-494.
• Eric Weisstein's World of Mathematics, Diophantine Equation 4th Powers.

Crossrefs

Cf. A003294, A176197.

Extensions

Corrected by Bo Asklund (boa(AT)mensa.se), Nov 05 2004

Corrected and extended by David Wasserman, Nov 16 2007