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Additive Diophantine inequalities with mixed powers II

  • Jörg Brüdern (a1)


A classical problem in the additive theory of numbers is the determination of the minimal s such that for all sufficiently large n the equation

is solvable in natural numbers xk. Improving on earlier results the author [2] has been able to prove that one may take s = 18. In a survey article W. Schwarz asked for an analogue for diophantine inequalities [6]. As a first contribution to this subject we prove

Theorem. Let λ2, …, λ23 be nonzero real numbers, λ23 irrational. Then the values taken by

at integer points ( x1, …, x22) are dense on the real line.



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Additive Diophantine inequalities with mixed powers II

  • Jörg Brüdern (a1)


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