# Thue’s lemma

Let $p$ be a prime number^{} of the form $4k+1$ . Then there are two unique integers $a$ and $b$ with $$ such that $p={a}^{2}+{b}^{2}$. Additionally, if a number $p$ can be written in as the sum of two squares in 2 different ways (i.e. $p={a}^{2}+{b}^{2}$ and $p={c}^{2}+{d}^{2}$ with the two sums being different), then the number $p$ is composite.

Title | Thue’s lemma |
---|---|

Canonical name | ThuesLemma |

Date of creation | 2013-03-22 13:19:05 |

Last modified on | 2013-03-22 13:19:05 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 8 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 11A41 |

Related topic | RepresentingPrimesAsX2ny2 |