A063923 Numbers k such that k^5 = a^5 + b^5 + c^5 + d^5 + e^5 has a nontrivial primitive solution in nonnegative integers.

72, 94, 107, 144, 365, 415, 427, 435, 480, 503, 530, 553, 575, 650, 700, 703, 716, 729, 744, 764, 804, 848, 851, 875, 923, 941, 975, 1004, 1006, 1040, 1044, 1235, 1257, 1313, 1327, 1329, 1369, 1392, 1457, 1469, 1504, 1528, 1537, 1575, 1583, 1588, 1596, 1623, 1653, 1685, 1686

Offset

1,1

Comments

Primitive means a solution for k has gcd(a,b,c,d,e) = 1. [Corrected by Jianing Song, Jan 24 2020]

Nontrivial means at least two of a,b,c,d,e are nonzero. - Jianing Song, Jan 24 2020

Links

Jianing Song, Table of n, a(n) for n = 1..400 (All terms from James Waldby link)

L. J. Lander, T. R. Parkin and J. L. Selfridge, A Survey of Equal Sums of Like Powers, Mathematics of Computation, Vol. 21, No. 99 (Jul., 1967), pp. 446-459. See Table III p. 449.

James Waldby, A Table of Fifth Powers equal to a Fifth Power

Index to sequences related to Diophantine equations (5,1,5)

Example

   72^5 = 19^5 + 43^5 + 46^5 + 47^5 +  67^5;
   94^5 = 21^5 + 23^5 + 37^5 + 79^5 +  84^5;
  107^5 =  7^5 + 43^5 + 57^5 + 80^5 + 100^5.

Crossrefs

Cf. A063922.

For cubes: A003072, A023041, A261029.

For fourth powers: A003828, A175610, A039664, A003294.

Sequence in context: A066943 A206264 A063922 * A030025 A245213 A270308

Adjacent sequences: A063920 A063921 A063922 * A063924 A063925 A063926

Keyword

nonn

Author

David W. Wilson, Aug 31 2001

Extensions

144 and 1006 inserted and name simplified by Jianing Song, Jan 24 2020

More terms from Jinyuan Wang, Jan 24 2020

Status

approved