Glasnik matematički, Vol. 50 No. 2, 2015.
Original scientific paper
https://doi.org/10.3336/gm.50.2.02
ON TWO OF JOHN LEECH'S UNSOLVED PROBLEMS CONCERNING RATIONAL CUBOIDS
Allan MacLeod
; Statistics, O.R. and Mathematics Group, University of the West of Scotland, High St., Paisley,, Scotland. PA1 2BE
Abstract
Let {X,Y,Z,A,B,C} ℚ+ be such that X2+Y2=A2, X2+Z2=B2 and Y2+Z2=C2. We consider the problem of finding T ℚ+ such that either
T2-X2=◻, T2-Y2=◻, T2-Z2=◻
or
T2-A2=◻, T2-B2=◻, T2-C2=◻.
We show that problem 2 always has a solution and we provide a formula for T. Extensive computation has been unable to find a single solution of problem 1.
Keywords
Rational cuboid; elliptic curve
Hrčak ID:
150129
URI
Publication date:
29.12.2015.
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