A230562 Smallest number that is the sum of 2 positive 4th powers in >= n ways.

0, 2, 635318657

Offset: 0

Author

Jonathan Sondow, Oct 25 2013

Keywords

• hard
• more
• nonn

Comments

Hardy and Wright say that a(3) is unknown.

Guy, 2004: "Euler knew that 635318657 = 133^4 + 134^4 = 59^4 + 158^4, and Leech showed this to be the smallest example. No one knows of three such equal sums."

Examples

			0 = (empty sum).
2 = 1^4 + 1^4.
635318657 = 59^4 + 158^4 = 133^4 + 134^4.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, D1
• G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 6th edition, 2008; section 21.11.

Links

• Carlos Rivera, Puzzle 103: N = a^4 + b^4 = c^4 + d^4

Crossrefs

Cf. A003824, A016078, A018786, A046881, A088687, A088848, A088849, A088867, A230561.