The step size updates to the least common multiple (LCM) of the moduli already satisfied because adding the LCM to a current solution preserves the remainders for all those moduli. Any increment divisible by all the current moduli will not change the remainder modulo any of them, and the LCM is the smallest positive such increment.
Conditions: A number currently satisfies a set of congruences.; The new step size must preserve the remainders for all those congruences.
The step size updates to the least common multiple (LCM) of the moduli already satisfied because adding the LCM to a current solution preserves the remainders for all those moduli. Any increment divisible by all the current moduli will not change the remainder modulo any of them, and the LCM is the smallest positive such increment.
Conditions: A number currently satisfies a set of congruences.; The new step size must preserve the remainders for all those congruences.
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.