A230562 - OEIS

%I #22 Mar 14 2015 10:10:50

%S 0,2,635318657

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

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

%C 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."

%D R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, D1

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 6th edition, 2008; section 21.11.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_103.htm">Puzzle 103: N = a^4 + b^4 = c^4 + d^4</a>

%e 0 = (empty sum).

%e 2 = 1^4 + 1^4.

%e 635318657 = 59^4 + 158^4 = 133^4 + 134^4.

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

%K hard,more,nonn

%O 0,2

%A _Jonathan Sondow_, Oct 25 2013