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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?

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?