Diophantine inequalities with mixed powers
Journal of Number Theory, 1977 AbstractIt is shown that λ1, λ2,…, λ6, μ are not all of the same sign and at least one ratio λiλj is irrational then the values taken by λ1x13 + ⋯ + λ6x63 + μy3 for integer values of x1 ,…, x6, y are everywhere dense on the real line. A similar result holds for expressions of the form λ1x13 + ⋯ + λ4x43 + μ1y12 + μ2y23.
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