J Austral Math Soc Ser A 51 pp33--49, 1991.

A Decomposition of Integer Vectors. IV

A. Schinzel

(Received 10 May 1989)

Abstract

Given m linearly independent vectors n₁, ..., n_m Î Z^k and an integer l Î [m, k] one proves the existence of l linearly independent vectors p₁, ..., p_l Î Z^k or q₁, ..., q_l Î Z^k of small size (suitably measured) such that the n_i's are linear combinations of p_j's with rational coefficients of q_j's with integer coefficients.

1980 AMS Subject Classification (1985 Revision): 11H41

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Authors

A. Schinzel: Instytut Matematyczny Polskiej Akademii Nauk, ul. Sniadeckich 8, Skrytka pocztowa Nr 137, 00-950 Warszawa, Poland.

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Last Modified: Mon Feb 3 9:46:10 2003