Perfect powers with few binary digits and related Diophantine problems, II

DOI10.1017/S0305004112000345zbMath1291.11016MaRDI QIDQ4649449

Michael A. Bennett, Maurice Mignotte, Yann Bugeaud

Publication date: 22 November 2012

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

linear forms in logarithmsperfect powersdigital expansions

Mathematics Subject Classification ID

Radix representation; digital problems (11A63) Exponential Diophantine equations (11D61) Linear forms in logarithms; Baker's method (11J86)

Related Items (13)

Products of integers with few nonzero digits ⋮ On the digital representation of smooth numbers ⋮ PERFECT POWERS WITH THREE DIGITS ⋮ Squares with Three Nonzero Digits ⋮ Effective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equations ⋮ The polynomial-exponential equation \(1 + 2^a + 6^b = y^q\) ⋮ On the digital representation of integers with bounded prime factors ⋮ A Hasse-type principle for exponential Diophantine equations and its applications ⋮ On the Diophantine equation \(1 + 2^a + x^b = y^n\) ⋮ On sparse perfect powers ⋮ On the binary digits of \(n\) and \(n^2\) ⋮ On a conjecture of Schäffer concerning the equation \(1^k + \ldots + x^k = y^n\) ⋮ Bennett's Pillai theorem with fractional bases and negative exponents allowed

Cites Work

• Two exponential Diophantine equations
• Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation
• The equations \(2^N\pm 2^M\pm 2^L=z^2\)
• Linear forms in two logarithms and interpolation determinants
• Linear forms in two logarithms and interpolation determinants II
• The diophantine equation x²=p^a±p^b+1
• Linear forms in p-adic logarithms and the Diophantine equation formula here

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