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Numbers k such that (65*k)^2 can be represented in exactly 4 ways as the sum of a positive square and a positive fourth power.
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%I #19 Sep 18 2021 16:45:58

%S 7225,28900,34225,65025,115600,136900,180625,235225,260100,308025,

%T 354025,395641,462400,547600,585225,722500,835635,855625,874225,

%U 940900,1040400,1221025,1232100,1416100,1422798,1582564,1625625,1677025,1849600,2088025,2117025,2190400

%N Numbers k such that (65*k)^2 can be represented in exactly 4 ways as the sum of a positive square and a positive fourth power.

%C All terms multiplied by 65 are in A346110. It is unknown whether A346110 contains terms not of this form.

%C From _Karl-Heinz Hofmann_, Aug 28 2021: (Start)

%C A346110(44,46,53,95,97) are not divisible by 65 (5*13), but these few terms are all divisible by 145 (5*29). For further information about divisibility, see the links to A346110 below. (End)

%H Hugo Pfoertner, <a href="/A346594/b346594.txt">Table of n, a(n) for n = 1..208</a>

%H Karl-Heinz Hofmann, <a href="/A346110/a346110_1.pdf">All valid {z,x1,y1,x2,y2,x3,y3,x4,y4} sets up to 10^9</a>

%H Karl-Heinz Hofmann, <a href="/A346110/a346110.gif">A 3D Animation of the solutions up to 10^9</a>

%Y Cf. A346110.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Jul 28 2021