Representations of Real Numbers as Sums and Products of Liouville Numbers
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چکیده
A real number x is a Liouville number if to each natural number m there corresponds a rational number hm/krn , with k n,> 1, such that 0 < I x hm/km , < ( 1/km)m Some years ago I showed (possibly jointly with Mahler), that every real number is the sum of two Liouville numbers . A proof of the proposition may now be in the literature, but I do not know of any reference . In any case, the following slightly stronger theorem is now needed (see [1] ), and therefore I publish a proof . THEOREM . To each real number t (t 0) there correspond Liouville numbers x, y, u, v such that
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