Theorem 4.4. Consider the linear congruence ax=b (mod m). If (a,m) = d, then this has a solution if and only if d | b. In which case, the congruence has exactly d many solutions, which are given by t₁t+m/₁t+2² m m t, ,t + 277,...t + (d − 1) ·t 777, d d' where t is the unique solution of the congruence x = (mod).
Theorem 4.4. Consider the linear congruence ax=b (mod m). If (a,m) = d, then this has a solution if and only if d | b. In which case, the congruence has exactly d many solutions, which are given by t₁t+m/₁t+2² m m t, ,t + 277,...t + (d − 1) ·t 777, d d' where t is the unique solution of the congruence x = (mod).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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