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European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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Zuerich, Switzerland
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130
2013
0
On a Divisibility Problem
Horst
Alzer
, WALDBRÖL, GERMANY
József
Sándor
Babes-Bolyai University, CLUJ-NAPOCA, ROMANIA
Divisibility, Euler totient, sum of divisors, Weierstrass product, inequalities
We prove that there are no integers $n\geq 2$ and $k\geq 2$ such that $n^k$ divides ${\varphi} (n^k)+{\sigma} _k(n)$. For $k=2$ this settles a conjecture of Adiga and Ramaswamy.
Number theory
215
220
10.4171/RSMUP/130-8
http://www.ems-ph.org/doi/10.4171/RSMUP/130-8