Discrete Structure20805 marksNumerical: Chinese remainder theoremChinese Remainder Theorem
Solve the system of following congruences using Chinese Remainder theorem: x = 2 (mod 3), x = 3 (mod 5), x = 2 (mod 7)
Solve the system of following congruences using Chinese Remainder theorem: x = 2 (mod 3), x = 3 (mod 5), x = 2 (mod 7) [5]
$$x \equiv 2 \pmod{3}, \quad x \equiv 3 \pmod{5}, \quad x \equiv 2 \pmod{7}$$ Remainders: $a1 = 2,\ a2 = 3,\ a3 = 2$ Moduli: $m1 = 3,\ m2 = 5,\ m3 = 7$ The moduli are pairwise coprime, so CRT guarantees a unique solution modulo their product. --- $$M = 3 \times 5 \times 7 = 105$$ --- $$M1 = \frac...