@article{12310,
  abstract     = {Let  be a sequence of points on an elliptic curve defined over a number field K. In this paper, we study the denominators of the x-coordinates of this sequence. We prove that, if Q is a torsion point of prime order, then for n large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two points P and Q on the elliptic curve, we prove a lower bound for the number of primes p such that P is in the orbit of Q modulo p.},
  author       = {Verzobio, Matteo},
  issn         = {0022-314X},
  journal      = {Journal of Number Theory},
  keywords     = {Algebra and Number Theory},
  number       = {4},
  pages        = {378--390},
  publisher    = {Elsevier},
  title        = {{Primitive divisors of sequences associated to elliptic curves}},
  doi          = {10.1016/j.jnt.2019.09.003},
  volume       = {209},
  year         = {2020},
}

@article{204,
  abstract     = {Let k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a bound[Formula presented] for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way.},
  author       = {Browning, Timothy D},
  issn         = {0022-314X},
  journal      = {Journal of Number Theory},
  number       = {2},
  pages        = {293 -- 318},
  publisher    = {Academic Press},
  title        = {{Equal Sums of Two kth Powers}},
  doi          = {10.1006/jnth.2002.2800},
  volume       = {96},
  year         = {2002},
}