What would you like to understand?

If two congruences x ≡ r (mod m) and x ≡ r (mod n) share the same remainder r, then $x = r$ is an immediate particular solution. The full combined solution set is then r plus multiples of the LCM of the two moduli: $x = r + k$ * LCM(m, n).

Conditions: The two congruences have the identical remainder r.; The moduli m and n are positive integers.

If two congruences x ≡ r (mod m) and x ≡ r (mod n) share the same remainder r, then $x = r$ is an immediate particular solution. The full combined solution set is then r plus multiples of the LCM of the two moduli: $x = r + k$ * LCM(m, n).

Conditions: The two congruences have the identical remainder r.; The moduli m and n are positive integers.