Because the step size and the modulus m are coprime, the sequence of remainders generated by adding the step size modulo m forms a complete cycle of length m. If the target remainder does not appear within the first m steps, it will never appear, meaning no solution exists for that specific congruence within the progression.
Conditions: The step size of the current arithmetic progression is coprime to the target modulus m.; The search is bounded by the modulus m.
Because the step size and the modulus m are coprime, the sequence of remainders generated by adding the step size modulo m forms a complete cycle of length m. If the target remainder does not appear within the first m steps, it will never appear, meaning no solution exists for that specific congruence within the progression.
Conditions: The step size of the current arithmetic progression is coprime to the target modulus m.; The search is bounded by the modulus m.
The general formula for the least common multiple (LCM) of two positive integers a and b is their product divided by their greatest common divisor (GCD): LCM(a,b) = (a∗b) / GCD(a,b).
The general formula for the least common multiple (LCM) of two positive integers a and b is their product divided by their greatest common divisor (GCD): LCM(a,b) = (a∗b) / GCD(a,b).