Mathegoras

Number theory › Congruences and modular arithmetic › Chinese remainder theorem

Solving a four-congruence CRT system

University · ●●●○○ 50 pts

Find the least nonnegative integer xx satisfying x≡4(mod5)x \equiv 4 \pmod{5}, x≡2(mod7)x \equiv 2 \pmod{7}, x≡2(mod11)x \equiv 2 \pmod{11} and x≡12(mod13)x \equiv 12 \pmod{13}.

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modular arithmeticsystems of congruencesmodular inverse