The Uniform Primality Conjecture for the Twisted Fermat Cubic Graham Everest, Ouamporn Phuksuwan and Shaun Stevens
نویسنده
چکیده
On the twisted Fermat cubic, an elliptic divisibility sequence arises as the sequence of denominators of the multiples of a single rational point. We prove that the number of prime terms in the sequence is uniformly bounded. When the rational point is the image of another rational point under a certain 3-isogeny, all terms beyond the first fail to be primes.
منابع مشابه
Primitive Divisors on Twists of the Fermat Cubic Graham Everest, Patrick Ingram and Shaun Stevens
We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u + v = m, with m cube-free, all the terms beyond the first have a primitive divisor. 1. Statement of Main Theorem Let C denote a twist of the Fermat cubic, C : U + V 3 = mW 3 (1) with m a non-zero rational number. If K denotes any field of characteristic zero, the set C(K) of projective K-rational points satisfy...
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