An elliptic sequence is not a sampled linear recurrence sequence
نویسندگان
چکیده
Let E be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let P = (x1/z 2 1 , y1/z 3 1) be a rational point of infinite order on E, where x1, y1, z1 are coprime integers. We show that the integer sequence (zn)n>1 defined by nP = (xn/z 2 n, yn/z 3 n) for all n > 1 does not eventually coincide with (un2)n>1 for any choice of linear recurrence sequence (un)n>1 with integer values.
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