Geodesic
Superpositions of elementary arithmetic functions
Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 33-48

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A new concise proof of the following theorem is found: the system of four functions $\{x+y,x\div y,\lfloor x/y\rfloor,2^x\}$ induces the class of Kalmar elementary functions. An elimination mode of bounded summation is used in the proof. 
@article{DA_2006_13_4_a3,
     author = {S. S. Marchenkov},
     title = {Superpositions of elementary arithmetic functions},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {33--48},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2006_13_4_a3/}
}
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S. S. Marchenkov. Superpositions of elementary arithmetic functions. Diskretnyj analiz i issledovanie operacij, Tome 13 (2006) no. 4, pp. 33-48. http://geodesic.mathdoc.fr/item/DA_2006_13_4_a3/