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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