Solving Systems of Congruences when mods not pairwise relatively prime

  • Thread starter CantorSet
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  • #1
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Main Question or Discussion Point

Hi folks,

The CRT says there's a unique solution to the system of congruences

[itex] x = a [/itex] (mod m)
[itex] x = b [/itex] (mod n)
[itex] x = c [/itex] (mod p)

in (mod mnp) when [itex] m, n, p [/itex] are pairwise relatively prime. But what if [itex] m, n, p [/itex] are NOT pairwise relatively prime. Is there a systematic way to solve these cases?
 

Answers and Replies

  • #2
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The system may not have a solution if the moduli are not pairwise coprime.We can, of course,solve two equations at a time modulo the lcm & try to patch up the solutions... I don't know how to answer this best.
 

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