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A200219
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Number of solutions of the equation x^n + (x+1)^n = (x+2)^n (mod n) for x = 0..n-1.
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2
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1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 0, 8, 1, 6, 1, 4, 1, 2, 1, 8, 0, 2, 9, 2, 1, 4, 1, 16, 0, 2, 0, 12, 1, 2, 0, 8, 1, 4, 1, 2, 3, 2, 1, 16, 7, 10, 2, 2, 1, 18, 0, 8, 0, 2, 1, 8, 1, 2, 3, 32, 2, 4, 1, 4, 0, 2, 1, 24, 1, 2, 0, 4, 6, 4, 1, 16, 27, 2, 1, 8
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OFFSET
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1,4
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COMMENTS
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a(n) = 0 for n = 15, 25, 33, 35, 39, 55, 57,… (see A200046).
a(n) = 1 if n prime.
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LINKS
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EXAMPLE
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a(6) = 2 because:
for x = 3, 3^6 + 4^6 == 1(mod 6) and 5^6 == 1(mod 6).
for x = 5, 5^6 + 6^6 == 1 (mod 6) and (7)^6 == 1 (mod 6).
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MAPLE
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for n from 1 to 100 do:ii:=0:for x from 0 to n-1 do:if x^n+(x+1)^n -(x+2)^n mod n=0 then ii:=ii+1:else fi:od: printf(`%d, `, ii):od:
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MATHEMATICA
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Array[Function[n, Count[Array[Mod[#^n+(#+1)^n-(#+2)^n, n]&, n, 0], 0]], 84]
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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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