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Let k be an integer with k ≥ 4 and η be any real number. Suppose that λ1,λ2,λ3,λ4,λ5 are nonzero real numbers, not all of the same sign and λ1/λ2… Click to show full abstract
Let k be an integer with k ≥ 4 and η be any real number. Suppose that λ1,λ2,λ3,λ4,λ5 are nonzero real numbers, not all of the same sign and λ1/λ2 is irrational. It is proved that the inequality |λ1p1 + λ2p22 + λ 3p33 + λ 4p44 + λ 5p5k + η| < max 1≤j≤5pj−σ has infinitely many solutions in prime variables p1,p2,p3,p4,p5, where 0 < σ < 5 288 for k = 4, and 0 < σ < 5 6k2(k+1) for k ≥ 5. This gives an improvement of the recent result.
Keywords:
diophantine inequality;
one diophantine;
inequality unlike;
inequality;
unlike powers;
prime variables
Journal Title: International Journal of Number Theory
Year Published: 2017
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Journal Title: International Journal of Number Theory
Year Published: 2017
Link to full text (if available)
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recommendations!