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New bounds and conditions for the equation of Nagell–Ljunggren

✍ Scribed by Preda Mihăilescu

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
193 KB
Volume
124
Category
Article
ISSN
0022-314X

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✦ Synopsis

The general case of the Nagell-Ljunggren equation is

= p e • y q , with x, y ∈ Z, e ∈ {0, 1}, and p = q odd primes. In this paper we derive a new bound q > f (p) for which there are no solutions. For small q the problem is harder and we achieve a conditional result: q h - p for q < g(p) and some additional condition on (p, q) must hold. Both functions f, g are quadratic and they leave a small gap for p 257, on which we have no general result. The picture is completed by some explicit, unconditional upper bounds for the absolute values |x|, |y|.

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✍ Chien-Hua Lee; Tsung-Lieh Hsien 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 96 KB 👁 2 views

New upper and lower matrix bounds and the corresponding eigenvalue bounds on the solution of the discrete algebraic Riccati equation are discussed in this paper. The present bounds are tighter than the majority of those found in the literature.