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A366419
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Number of distinct integers of the form (x^n + y^n) mod n^3.
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3
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1, 5, 15, 11, 65, 21, 133, 34, 135, 75, 561, 63, 949, 192, 975, 129, 1921, 165, 3097, 99, 525, 663, 6095, 231, 1625, 741, 1215, 576, 8149, 525, 12121, 513, 8415, 2091, 8645, 495, 21349, 3081, 2535, 363, 34481, 315, 32551, 1989, 8775, 5316, 51935, 903, 6517, 1875, 28815, 1062
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OFFSET
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1,2
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COMMENTS
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It is enough to take x,y from {0,1,...,n^2-1}.
It appears that the number of distinct integers of the form x^(p^k) + y^(p^k) mod (p^k)^m for a prime p>2 and natural k is A121278(p)*p^(k-1)*p^(k*(m-2)) for m>1. For m=1 see A366418.
It appears that the number of distinct integers of the form x^n + y^n mod n^m for an odd n, m>1 is A121278(n)*n^(m-2).
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LINKS
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PROG
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(PARI) a(n) = #setbinop((x, y)->Mod(x, n^3)^n+Mod(y, n^3)^n, [0..n^2-1]); \\ Michel Marcus, Oct 14 2023
(Python)
m = n**3
return len({(pow(x, n, m)+pow(y, n, m))%m for x in range(n**2) for y in range(x+1)}) # Chai Wah Wu, Nov 13 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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