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<p>We study solutions of an equation of the form <i>a</i> ∙ <i>x</i> = <i>b</i> in the homomorphic image of an adequate ring. It is known that the greatest common divisor of all roots of this equation is also its root. It is shown that the family of solutions of this equation contains, in particular, the solutions that are divisible by the remaining roots of the equation and, moreover, these solutions are mutually associated with each other.</p>

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Arithmetic Properties of the Solutions of Linear Equations

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • V. P. Shchedryk

摘要

We study solutions of an equation of the form a ∙ x = b in the homomorphic image of an adequate ring. It is known that the greatest common divisor of all roots of this equation is also its root. It is shown that the family of solutions of this equation contains, in particular, the solutions that are divisible by the remaining roots of the equation and, moreover, these solutions are mutually associated with each other.