Geodesic
Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number
Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 667-675.

Voir la notice de l'article provenant de la source Math-Net.Ru

It is known that the arithmetic of natural and integer numbers is unsolvable. Even the universal theory of integers with addition and multiplication is unsolvable. It is proved herein that an elementary theory of integers with addition, order, and multiplication by one arbitrary number is solvable and multiplication by the power of one number is unsolvable. For a certain $n$, the universal theory of integers with addition and $n$ multiplications by an arbitrary number is also unsolvable. 
@article{MZM_1973_13_5_a4,
     author = {Yu. G. Penzin},
     title = {Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number},
     journal = {Matemati\v{c}eskie zametki},
     pages = {667--675},
     publisher = {mathdoc},
     volume = {13},
     number = {5},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a4/}
}
TY  - JOUR
AU  - Yu. G. Penzin
TI  - Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number
JO  - Matematičeskie zametki
PY  - 1973
SP  - 667
EP  - 675
VL  - 13
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a4/
LA  - ru
ID  - MZM_1973_13_5_a4
ER  - 
%0 Journal Article
%A Yu. G. Penzin
%T Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number
%J Matematičeskie zametki
%D 1973
%P 667-675
%V 13
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a4/
%G ru
%F MZM_1973_13_5_a4
Yu. G. Penzin. Solvability of the theory of integers with addition, order, and multiplication by an arbitrary number. Matematičeskie zametki, Tome 13 (1973) no. 5, pp. 667-675. http://geodesic.mathdoc.fr/item/MZM_1973_13_5_a4/