

A003824


Numbers that are the sum of two 4th powers in more than one way (primitive solutions).


10



635318657, 3262811042, 8657437697, 68899596497, 86409838577, 160961094577, 2094447251857, 4231525221377, 26033514998417, 37860330087137, 61206381799697, 76773963505537, 109737827061041, 155974778565937
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OFFSET

1,1


COMMENTS

The prime divisors of elements of A003824 all appear to be in A045390.  David W. Wilson, May 28 2010
Conjecture: a(n) is congruent to 1,2,10 or 17 mod 24.  Mason Korb, Oct 07 2018


REFERENCES

L. E. Dickson, History of The Theory of Numbers, Vol. 2 pp. 6447, 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 bfile 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), 778780.
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. 155157) 1991.
Eric Weisstein's World of Mathematics, Diophantine equations, 4th powers


CROSSREFS

Cf. A018786.
Sequence in context: A251498 A233848 A018786 * A105382 A032432 A271770
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



