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Start Over Creator Alzer, Horst

1. Diophantine equations involving factorials

Creator:
Alzer, Horst and Luca, Florian
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Diophantine equation and factorial
Language:
English
Description:
We study the Diophantine equations (k!)n − k n = (n!)k − n k and (k!)n + k n = (n!)k + n k , where k and n are positive integers. We show that the first one holds if and only if k = n or (k, n) = (1, 2), (2, 1) and that the second one holds if and only if k = n.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On Ozeki’s inequality for power sums

Creator:
Alzer, Horst
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
math and power sums
Language:
English
Description:
et $p\in (0,1)$ be a real number and let $n\ge 2$ be an even integer. We determine the largest value $c_n(p)$ such that the inequality \[ \sum ^n_{i=1} |a_i|^p \ge c_n(p) \] holds for all real numbers $a_1,\ldots ,a_n$ which are pairwise distinct and satisfy $\min _{i\ne j} |a_i-a_j| = 1$. Our theorem completes results of Ozeki, Mitrinović-Kalajdžić, and Russell, who found the optimal value $c_n(p)$ in the case $p>0$ and $n$ odd, and in the case $p\ge 1$ and $n$ even.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

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