Apollonian Numbers

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1939 English Publisher:Informa UK LimitedJournal:The Mathematical Gazette, volume 23, pages 451-455 (issn: 0025-5572, eissn: 2056-6328,

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Authors: Paradine, C. G.;

doi: 10.2307/3607001

Apollonian Numbers

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Abstract

In two recent Notes (1354 and 1289) formulae have been given for the determination of some, but not all, triangles having integral sides and one integral median. All such triangles can be found, with the aid of a list of primes of the form 4 n + 1. From the equation AB 2 + AC 2 = 2 AD 2 + 2 BD 2 it follows that if AB, AC and AD are to be integral, then 2 BD 2 is an integer, whence, if BC is to be integral, BD is an integer.

Keywords

Apollonian numbers, Elementary number theory

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