Publication date
June 2007
DOI Publisher
Elsevier Inc. ISSN
0022-314X Citation count (estimate)
6Abstract
AbstractThe general case of the Nagell–Ljunggren equation isxp−1x−1=pe⋅yq,withx,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∤hp− 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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