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A028942
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Negative of numerator 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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8
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0, 0, 1, 3, 5, -14, -8, 69, 435, 2065, 3612, -28888, 43355, 2616119, 28076979, -332513754, -331948240, 8280062505, 641260644409, 18784454671297, 318128427505160, -10663732503571536, -66316334575107447, 8938035295591025771
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OFFSET
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1,4
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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 negated numerators of the y_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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3P = (-1, -1),
4P = (2, -3),
5P = (1/4, -5/8),
6P = (6, 14).
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PROG
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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