Simultaneous Congruences with Non-Coprime Divisors

Definition

Simultaneous Congruences with Non-Coprime Divisors in plain English

Pull Simultaneous Congruences with Non-Coprime Divisors when a Chinese-remainder style system where the moduli share a factor. Clues include System of congruences, non-coprime moduli. Blueprint: Apply the GCD consistency test. If it passes, solve on the LCM modulus, not the raw product of the moduli. Why it beats the long way: Blind CRT assumes coprime moduli and invents fake unique answers. Micro-example: n equiv 4 pmod6 and n equiv 10 pmod15. gcd(6,15)=3, and 4 equiv 10 pmod3, so solutions exist on modulus mathrmLCM(6,15)=30. One solution is 10; then 10+30k.

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