Abstract
A general solution, containing n-1 arbitrary integers, of linear Diophantine equation with n unknowns is presented in terms of parameters of n-1 Euclidean algorithms. Construction procedures of general and natural solutions based on application of ``truncated'' parameters of Euclidean algorithms are described. Domains of equation right-hand part values guaranteeing existence of a given number of natural solutions are found. Explicit formulae for natural solutions are presented. Some illustrations are given.