p. 65 - 72 Homoroot integer numbers
M. H. Hooshmand Received: November 11, 2008;
Revised: April 24, 2009;
Accepted: September 8, 2009
Abstract.
In this paper we first define homorooty between two integer
numbers and study some of their properties. There after we shall
state some applications of the homorooty in studying and solving
some Diophantine equations and systems, as an interesting and
useful elementary method. Also by the homorooty, we state and
prove the necessary and sufficient conditions for existence of
finite solutions in a special case of the quartic equation and
evaluate the bounds of its solutions.
Keywords:
Diophantine equation and system; homorooty; homoroot integers;
quartic equation; homorooty inequality; homorooty lemma.
AMS Subject classification:
Primary: 11A99, 11D25, 11D09, 11D72
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