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Diophantine inequalities with mixed powers
Authors:R.C Baker  G Harman
Affiliation:Department of Mathematics, Royal Holloway College, Egham, Surrey TW20 OEX, England
Abstract:It is shown that if λ1,…, λ6 are nonzero real numbers, not all of the same sign, such that λ1λ2 is irrational, then the values taken by λ1x12 + λ2x22 + λ3x33 + λ4x43 + λ5x55 + λ6x65 for integral x1,…, x6 are everywhere dense on the real line. Similar results are proved with other combinations in place of the two fifth powers.
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