|
| |
|
|
A003824
|
|
Numbers that are the sum of two 4th powers in more than one way (primitive solutions).
|
|
9
|
|
|
|
635318657, 3262811042, 8657437697, 68899596497, 86409838577, 160961094577, 2094447251857, 4231525221377, 26033514998417, 37860330087137, 61206381799697, 76773963505537, 109737827061041, 155974778565937
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The prime divisors of elements of A003824 all appear to be in A045390. - David W. Wilson, May 28 2010
|
|
|
REFERENCES
|
L. E. Dickson, History of The Theory of Numbers, Vol. 2 pp. 644-7, Chelsea NY 1923.
R. K. Guy, Unsolved Problems in Number Theory, D1.
|
|
|
LINKS
|
D. Wilson, Table of n, a(n) for n = 1..516 [The b-file was computed from Bernstein's list]
D. J. Bernstein, List of 516 primitive solutions p^4 + q^4 = r^4 + s^4 = a(n)
D. J. Bernstein, Enumerating solutions to p(a) + q(b) = r(c) + s(d)
D. J. Bernstein, sortedsums (contains software for computing this and related sequences)
J. Leech, Some solutions of Diophantine equations, Proc. Camb. Phil. Soc., 53 (1957), 778-780.
Carlos Rivera, Puzzle 103
E. Rosenstiel et al., The Four Least Solutions in Distinct Positive Integers of the Diophantine Equation s = x^3 + y^3 = z^3 + w^3 = u^3 + v^3 = m^3 + n^3, Instit. of Mathem. and Its Applic. Bull. Jul 27 (pp. 155-157) 1991.
Eric Weisstein's World of Mathematics, Diophantine equations, 4th powers
|
|
|
CROSSREFS
|
Cf. A018786.
Sequence in context: A251498 A233848 A018786 * A105382 A032432 A234071
Adjacent sequences: A003821 A003822 A003823 * A003825 A003826 A003827
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
More terms from David W. Wilson, Aug 15 1996
|
|
|
STATUS
|
approved
|
| |
|
|