formula_22 and formula_124 are congruent (written formula_125 mod formula_1) when they have the same remainder after division by formula_1. However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number formula_128 as modulus, division by formula_129 is possible: formula_130, because clearing denominators by multiplying both sides by formula_129 gives the valid formula formula_132. However, with the composite modulus formula_133, division by formula_129 is impossible. There is no valid solution to formula_135: clearing denominators by multiplying by formula_129 causes the left-hand side to become formula_137 while the right-hand side becomes either formula_138 or formula_129.