Leonid Vaserstein

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This paper was motivated by the following open problem ([8], p.390): “CNTA 5.15 (Frits Beukers). Prove or disprove the following statement: There exist four polynomials A,B,C,D with integer coefficients (in any number of variables) such that AD−BC = 1 and all integer solutions of ad−bc = 1 can be obtained from A,B,C,D by specialization of the variables to(More)
It is well known that every l∞ linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to an l∞ linear approximation problem. Now we recall relevent definitions. An affine function of variables x1, . . . , xn is b0 + c1x1 + · · · + cnxn where b0, ci are given numbers. A(More)
with unknown xi. In 1769 Euler conjectured that (1.1) has no positive integral solutions when m < n. This generalizes both his result for n1⁄4 3 and Fermat’s Last Theorem. However his conjecture was refuted for mþ 11⁄4 n1⁄4 5 (Lander and Parkin, 1966) and then for mþ 11⁄4 n1⁄4 4 (Elkies, 1988). It is still unknown whether (1.1) has solutions with mþ 11⁄4 n(More)
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