### Abstract

We show that the number of integer points on an elliptic curve y^{2} = f(x) with X_{0} < x ≤ X_{0} + X is 蠐 X^{1/2} where the implicit constant depends at most on the degree of f(x). This improves on various bounds of Cohen [4], Bombieri and Pila [1] and of Pila [9], and others. In particular it follows that the number of positive integral solutions to x^{3} + y^{2} = n is 蠐 n^{1/6}.

Original language | English (US) |
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Pages (from-to) | 1377-1382 |

Number of pages | 6 |

Journal | Rocky Mountain Journal of Mathematics |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2014 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)