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Akademický článek

MOSER'S MATHEMAGICAL WORK ON THE EQUATION 1 k + 2 k + · · · + (m - 1) k = m k

Autor: MOREE, PIETER

Publikováno v: The Rocky Mountain Journal of Mathematics, 2013 Jan 01. 43(5), 1707-1737.

Externí odkaz: https://www.jstor.org/stable/44240272

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Moser's mathemagical work on the equation 1^k+2^k+...+(m-1)^k=m^k

Autor: Moree, Pieter

Publikováno v: Rocky Mountain J. Math. 43 (2013), 1707--1737

If the equation of the title has an integer solution with k>=2, then m>10^{10^6}. Leo Moser showed this in 1953 by amazingly elementary methods. With the hindsight of more than 50 years his proof can be somewhat simplified. We give a further proof sh

Externí odkaz: http://arxiv.org/abs/1011.2940

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The Erd\H{o}s--Moser equation $1^k+2^k+...+(m-1)^k=m^k$ revisited using continued fractions

Autor: Gallot, Yves, Moree, Pieter, Zudilin, Wadim

Publikováno v: Math. Comp. 80 (2011), no. 274, 1221--1237

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 $m>10^{10^7}$. H

Externí odkaz: http://arxiv.org/abs/0907.1356

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