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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).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 m m ‚t+277₁...t+ (d − 1) d't+27/0 7/7, d d' where t is the unique solution of the congruence x = (mod). t, t₁t+m/₁t+
Transcribed Image Text: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 m m ‚t+277₁...t+ (d − 1) d't+27/0 7/7, d d' where t is the unique solution of the congruence x = (mod). t, t₁t+m/₁t+
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