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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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