Dasgupta, S; Voight, J, Sylvester’s problem and mock heegner points,
Proceedings of the American Mathematical Society, vol. 146 no. 8
(January, 2018),
pp. 3257-3273, American Mathematical Society (AMS)
(last updated on 2024/04/23)
Abstract:
We prove that if p ≡ 4, 7 (mod 9) is prime and 3 is not a cube modulo p, then both of the equations x3 + y3 = p and x3 + y3 = p2 have a solution with x, y ∈ ℚ.