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A331675 Numbers k such that k^4 = a^4 + b^4 + c^4 + d^4 has at least two positive primitive solutions.

%I A331675 #17 Jan 27 2020 02:01:35
%S A331675 31127,41963,72899,154789,195479,208471
%N A331675 Numbers k such that k^4 = a^4 + b^4 + c^4 + d^4 has at least two positive primitive solutions.
%C A331675 Primitive solutions means gcd(a,b,c,d) = 1.
%C A331675 These are all terms from Jaroslaw Wroblewski link, which gives all positive solutions to k^4 = a^4 + b^4 + c^4 + d^4 where k < 222000, gcd(a,b,c,d) = 1.
%H A331675 Jaroslaw Wroblewski, <a href="http://www.math.uni.wroc.pl/~jwr/eslp/414.txt">Exhaustive list of 1009 solutions to (4,1,4) below 222,000</a> (Note: (t,m,n) denotes the equation Sum_{i=1..m} (a_i)^t = Sum_{j=1..n} (b_j)^t, where a_i, b_j are positive integers, gcd(a_1, a_2, ..., a_m, b_1, b_2, ..., b_n) = 1.)
%e A331675 Solutions to k^4 = a^4 + b^4 + c^4 + d^4 = a'^4 + b'^4 + c'^4 + d'^4:
%e A331675 31127: (2260, 4870, 17386, 30335), (2495, 11998, 16430, 30320);
%e A331675 41963: (1100, 17260, 25015, 40234), (8750, 12109, 14470, 41720);
%e A331675 72899: (4555, 44270, 58868, 59330), (9700, 16480, 47618, 69265);
%e A331675 154789: (49586, 55450, 102170, 145615), (66405, 106740, 119760, 121664);
%e A331675 195479: (12970, 43340, 140947, 180520), (25570, 41080, 112822, 189695);
%e A331675 208471: (3903, 46560, 61290, 207950), (91045, 149222, 150550, 168730).
%Y A331675 Subsequence of A039664 (and thus of A003294).
%Y A331675 Other similar sequences:
%Y A331675 A023041 (k^3=a^3+b^3+c^3, gcd(a,b,c)=1);
%Y A331675 A003828 (k^4=a^4+b^4+c^4, gcd(a,b,c)=1);
%Y A331675 A175610 (k^4=a^4+b^4+c^4);
%Y A331675 A134341 (k^5=a^5+b^5+c^5+d^5);
%Y A331675 A063923 (k^5=a^5+b^5+c^5+d^5+e^5, gcd(a,b,c,d,e)=1);
%Y A331675 A063922 (k^5=a^5+b^5+c^5+d^5+e^5);
%Y A331675 A331674 (k^5=a^5+b^5+c^5+d^5+e^5, gcd(a,b,c,d,e)=1, at least two solutions).
%K A331675 nonn,hard,more
%O A331675 1,1
%A A331675 _Jianing Song_, Jan 24 2020