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Apollonian Numbers

Published online by Cambridge University Press:  03 November 2016

C. G Paradine
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Extract

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 4n + 1.

From the equation AB 2 + AC 2 = 2AD 2 + 2BD 2 it follows that if AB, AC and AD are to be integral, then 2BD 2 is an integer, whence, if BC is to be integral, BD is an integer.

Type
Research Article
Information
The Mathematical Gazette , Volume 23 , Issue 257 , December 1939 , pp. 451 - 455
Copyright
Copyright © Mathematical Association 1939

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