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A367643
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Number of equivalence classes of degree n integer polynomials whose discriminants are powers of 2 (in absolute value).
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1
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OFFSET
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1,2
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COMMENTS
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Here, two degree n integer polynomials f(x) and g(x) are considered equivalent if there exist integers a, b, c, d such that a*d - b*c is not zero and (cx+d)^n * f((ax+b)/(cx+d)) is some nonzero rational multiple of g(x).
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LINKS
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EXAMPLE
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For n = 1, every linear (degree 1) polynomial is equivalent to x and has discriminant 1, so a(1) = 1.
For n = 2, the a(2) = 4 equivalence classes are represented by the degree 2 polynomials x^2 + x, x^2 + 1, x^2 + 2, and x^2 - 2. These have discriminants 1, -4, -8, and 8 respectively.
For n = 3, the a(3) = 4 equivalence classes are represented by the degree 3 polynomials x^3 + x, x^3 - x, x^3 + 2*x, and x^3 - 2*x. These have discriminants -4, 4, -32, and 32 respectively.
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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