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Numbers k such that k^4 can be written as a sum of four positive 4th powers with no common factor.
10

%I #20 Jun 01 2024 09:40:43

%S 353,651,2487,2501,2829,3723,3973,4267,4333,4449,4949,5281,5463,5491,

%T 5543,5729,6167,6609,6801,7101,7209,7339,7703,8373,8433,8493,8517,

%U 8577,8637,9137,9243,9431,9519,9639,9797,9877,10419,10939,11681,11757

%N Numbers k such that k^4 can be written as a sum of four positive 4th powers with no common factor.

%H T. D. Noe, <a href="/A039664/b039664.txt">Table of n, a(n) for n = 1..1003</a> (from Wroblewski, with duplicate n removed)

%H L. J. Lander, T. R. Parkin and J. L. Selfridge, <a href="http://links.jstor.org/sici?sici=0025-5718%28196707%2921%3A99%3C446%3AASOESO%3E2.0.CO%3B2-7">A survey of equal sums of like powers</a>, Math. Comp. vol. 21 no. 99, 1967, pp. 446-459, Table 1.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DiophantineEquation4thPowers.html">Diophantine Equation - 4th powers</a>

%H Jaroslaw Wroblewski, <a href="http://www.math.uni.wroc.pl/~jwr/eslp/414.txt">Exhaustive list of 1009 solutions to (4,1,4) below 222,000</a>

%Y Cf. A003294 (nonprimitive solutions allowed), A096739.

%K nonn

%O 1,1

%A _Felice Russo_

%E Edited by _Don Reble_, Jul 07 2007

%E Qualifier "positive" added to the name by _Jianing Song_, Jan 24 2020