chinese remainder theorem online solver
How do you find the solution of the Chinese remainder theorem?
x = 233.
On further simplification we get, 23 ≡ 2(mod 3); 23 ≡ 3(mod 5); 23 ≡ 2(mod 7) ∵ 233 ≡ 23(mod 105) and 23 is the smallest solution.How to solve 233 mod 105?
The Chinese remainder theorem says we can uniquely solve every pair of congruences having relatively prime moduli. x ≡ a mod m, x ≡ b mod n has a solution, and this solution is uniquely determined modulo mn.
What is important here is that m and n are relatively prime.
There are no constraints at all on a and b.What is the Chinese remainder theorem for two equations?
We now seek a multiplicative inverse for each mi modulo ni.
First: m1 ≡ 77 ≡ 2 (mod5), and hence an inverse to m1 mod n1 is y1 = 3.
Second: m2 ≡ 55 ≡ 6 (mod 7), and hence an inverse to m2 mod n2 is y2 = 6.
Third: m3 ≡ 35 ≡ 2 (mod 11), and hence an inverse to m3 mod n3 is y3 = 6.
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