The Erdős--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions

Mathematics – Number Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

17 pages

Scientific paper

10.1090/S0025-5718-2010-02439-1

If the equation of the title has an integer solution with $k\ge2$, then $m>10^{9.3\cdot10^6}$. 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 $m>10^{10^7}$. Here we achieve $m>10^{10^9}$ by showing that $2k/(2m-3)$ is a convergent of $\log2$ and making an extensive continued fraction digits calculation of $(\log2)/N$, with $N$ an appropriate integer. This method is very different from that of Moser. Indeed, our result seems to give one of very few instances where a large scale computation of a numerical constant has an application.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

The Erdős--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Erdős--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Erdős--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-319939

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.