The Erdős–Moser equation $1^{k}+2^{k}+\dots+(m-1)^{k}=m^{k}$ revisited using continued fractions
نویسندگان
چکیده
منابع مشابه
Revisited Using Continued Fractions
If the equation of the title has an integer solution with k ≥ 2, then m > 109.3·10 6 . This was the current best result and proved using a method due to L. Moser (1953). This approach cannot be improved to reach the benchmark m > 1010 7 . Here we achieve m > 1010 9 by showing that 2k/(2m−3) is a convergent of log 2 and making an extensive continued fraction digits calculation of (log 2)/N , wit...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2011
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-2010-02439-1