### Abstract

In this paper we explore equilateral triangles with integer coordinates vertices lying on the plane a x + b y + c z = 0 where coefficients a, b, c satisfy the Diophantine equation a^{2} + b^{2} + c^{2} = 3d^{2} for some integer!. If the plane is translated with any integer translation vector, we find planes which also containing equilateral triangles with integer coordinates vertices. Based on that knowledge from some previous studies, another parametric equations for integer coordinates vertices of equilateral triangle in ^{3} are constructed.

Original language | English |
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Article number | 012037 |

Journal | Journal of Physics: Conference Series |

Volume | 1442 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Jan 2020 |

Event | Basic and Applied Sciences Interdisciplinary Conference 2017, BASIC 2017 - , Indonesia Duration: 18 Aug 2017 → 19 Aug 2017 |