Geodesic
Parametric equations in free groups
Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 569-581.

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We introduce the notion of a parametric equation in a free group; this is an equation containing natural parameters as exponents and a system of linear Diophantine equations relating these exponents. For these equations, we introduce elementary transformations that are necessary for the description of general solutions of ordinary equations in a free group. We prove that it is possible to linearize any relation among parameters that appears in the course of transformations of the given equation. 
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     author = {Yu. I. Ozhigov},
     title = {Parametric equations in free groups},
     journal = {Matemati\v{c}eskie zametki},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/}
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Yu. I. Ozhigov. Parametric equations in free groups. Matematičeskie zametki, Tome 58 (1995) no. 4, pp. 569-581. http://geodesic.mathdoc.fr/item/MZM_1995_58_4_a8/

[1] Lyndon R. C., “Equations in free groups”, Trans. Amer. Math. Soc., 96 (1960), 445–457 | DOI | MR | Zbl

[2] Ozhigov Yu. I., “Uravneniya s dvumya neizvestnymi v svobodnoi gruppe”, DAN SSSR, 268:4 (1983), 808–814 | MR

[3] Razborov A. A., O sistemakh uravnenii v svobodnoi gruppe, Diss. ...kand. fiz.-mat. nauk, MGU, M., 1987