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 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |