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

Author

David W. Wilson, Aug 31 2001

Keywords

• nonn

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

Examples

			   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.
		

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)

Crossrefs

Cf. A063922.

For cubes: A003072, A023041, A261029.

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

Extensions

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

More terms from Jinyuan Wang, Jan 24 2020