Geodesic
Additional information concerning the content of the product of polynomials
Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 395-398

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Let $\operatorname{Cont}_Af$ denote the content of the polynomial $f$ in several unknowns with coefficients from the extension $R$ of the ring $A$. We prove that for arbitrary polynomials $f$ and $g$ the relation $$ \operatorname{Cont}\nolimits_Afg\cdot(\operatorname{Cont}g)^m=\operatorname{Cont}f\cdot(\operatorname{Cont}g)^{m+1}, $$ holds, where $m+1$ is the number of the nonzero terms of the polynomial $f$. 
@article{MZM_1974_16_3_a5,
     author = {A. I. Uzkov},
     title = {Additional information concerning the content of the product of polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {395--398},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a5/}
}
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A. I. Uzkov. Additional information concerning the content of the product of polynomials. Matematičeskie zametki, Tome 16 (1974) no. 3, pp. 395-398. http://geodesic.mathdoc.fr/item/MZM_1974_16_3_a5/