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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)



The prime divisors of elements of A003824 all appear to be in A045390. - David W. Wilson, May 28 2010


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.


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


Cf. A018786.

Sequence in context: A251498 A233848 A018786 * A105382 A032432 A271770

Adjacent sequences:  A003821 A003822 A003823 * A003825 A003826 A003827




N. J. A. Sloane


More terms from David W. Wilson, Aug 15 1996



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Last modified November 22 05:36 EST 2017. Contains 295076 sequences.