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.