ANTS-IX was the ninth edition of the biennial International Symposium on Algorithmic Number Theory. The ?rst edition of this symposium was held at Cornell University in 1994. ANTS-IX was held July 19-23, 2010 at INRIA in Nancy, France. The ANTS-IX Program Committee consisted of 12 members whose names are listed on the next page. The selection of the accepted papers among the submissions was made from mid-January to end of March 2010. Each paper was thoroughly reviewed by at least two experts, including a Program Committee member. The Program Committee selected 25 high-quality articles, which are excellent representatives of the current state of the art in various areas of - gorithmic number theory. The Selfridge Prize in computational number theory was awarded to the authors of the best contributed paper presented at the c- ference. We gratefully thank the authors of all submitted papers for their hard work which made the selection of a varied program possible. We also thank the authors of the accepted papers for their cooperation in the timely production of the revised versions. Each submitted paper was presented by one of its co-authors at the c- ference. Besides contributed papers, the conference included ?ve invited talks by Henri Darmon (McGill University), Jean-Fran, cois Mestre (Universit'eParis 7), Gabriele Nebe (RWTH Aachen), Carl Pomerance (Dartmouth College), and Oded Regev (Tel-Aviv University).
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