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A028943
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Denominator of y coordinate of n*P where P is the generator [0,0] for rational points on curve y^2+y = x^3-x.
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11
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1, 1, 1, 1, 8, 1, 27, 125, 343, 64, 12167, 24389, 205379, 2146689, 30959144, 274625, 3574558889, 50202571769, 553185473329, 4302115807744, 578280195945297, 1469451780501769, 238670664494938073, 13528653463047586625
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OFFSET
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1,5
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COMMENTS
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We can take P = P[1] = [x_1, y_1] = [0,0]. Then P[n] = P[1]+P[n-1] = [x_n, y_n] for n >= 2. Sequence gives numerators of the x_n. - N. J. A. Sloane, Jan 27 2022
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REFERENCES
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A. W. Knapp, Elliptic Curves, Princeton 1992, p. 77.
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LINKS
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FORMULA
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P=(0, 0), 2P=(1, 0), if kP=(a, b) then (k+1)P=(a'=(b^2-a^3)/a^2, b'=-1-b*a'/a).
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EXAMPLE
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5P = (1/4, -5/8).
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PROG
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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