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Number of integer solutions to n = x^k - y^k with x > y >= 0 and k >= 2.
2

%I #11 Nov 19 2020 22:34:19

%S 0,1,1,1,0,2,2,2,0,1,1,1,0,3,3,1,0,2,1,2,0,1,2,2,1,3,1,1,0,2,3,2,0,2,

%T 2,2,0,2,2,1,0,1,1,3,0,1,3,2,0,2,1,1,0,2,3,2,0,1,2,2,0,5,5,3,0,1,1,2,

%U 0,1,3,1,0,3,1,2,0,1,4,4,0,1,2,2,0,2,2

%N Number of integer solutions to n = x^k - y^k with x > y >= 0 and k >= 2.

%C a(n) = 0 for all n in A303744.

%C Records occur at n = 2, 3, 7, 15, 63, 240, 480, 720, 960, 1440, 2400, 2880, 3360, 4032, 5040, ... - _Peter Kagey_, Nov 18 2020

%H Peter Kagey, <a href="/A333880/b333880.txt">Table of n, a(n) for n = 2..10000</a>

%e For n = 63, the a(63) = 5 solutions are

%e 8^2 - 1^2 = 64 - 1,

%e 12^2 - 9^2 = 144 - 81,

%e 32^2 - 31^2 = 1024 - 961,

%e 4^3 - 1^3 = 64 - 1, and

%e 2^6 - 1^6 = 64 - 1.

%Y Cf. A034178, A303744, A333822, A333868.

%K nonn

%O 2,6

%A _Peter Kagey_, Apr 08 2020