Finding integers k for which a given Diophantine equation has no solution in kth powers of integers

@article{Granville1992FindingIK,
  title={Finding integers k for which a given Diophantine equation has no solution in kth powers of integers},
  author={A. Granville},
  journal={Acta Arithmetica},
  year={1992},
  volume={60},
  pages={203-212}
}
  • A. Granville
  • Published 1992
  • Mathematics
  • Acta Arithmetica
  • (1) f(x1 , x k 2 , . . . , x k n) = 0 has solutions in non-zero integers x1, x2, . . . , xn. For homogeneous diagonal f of degree one, Davenport and Lewis [DL] showed that k ∈ T (f) whenever (n − 1) ≥ k ≥ 18; however, Ankeny and Erdős [AE] showed that T (f) has zero density in the set of all positive integers provided that all distinct subsets of the set of coefficients of f have different sums. For general polynomials f , Ribenboim [Ri] showed that certain values of k cannot belong to T (f… CONTINUE READING
    2 Citations
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    On Diagonal Equations over Finite Fields
    • 9

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