Geodesic
A cyclic sum with 12 terms
Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 873-885 
E. K. Godunova; V. I. Levin. A cyclic sum with 12 terms. Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 873-885. http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a7/
@article{MZM_1976_19_6_a7,
     author = {E. K. Godunova and V. I. Levin},
     title = {A~cyclic sum with 12 terms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {873--885},
     year = {1976},
     volume = {19},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a7/}
}
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%A V. I. Levin
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%J Matematičeskie zametki
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Voir la notice de l'article provenant de la source Math-Net.Ru

The inequality $$ \sum_{i=1}^{12}\frac{x_i}{x_{i+1}+x_{i+2}}\ge6 $$ is proved for all $x_i\ge0$, $x_i+x_{i+1}>0$ where $x_{12+i}=x_i$