The "abc conjecture" is an important unsolved theorem of number theory, it concerns equations with one or more unknowns. The conjecture is formulated as follows: we take three integers a, b and c which are prime to each other, i.e. which have no common factors except 1 and which satisfy the relation a+b=c. If d=radd(abc) is defined as the product of the distinct factors of abc, the conjecture states that d is "rarely" smaller than c. In order to be able to compare the mathematical result of two equations, it is necessary to give a well-defined mathematical meaning to the "rarely" and this work seeks, finds and mathematically defines the value that the "rarely" reported in the statement must have; only by knowing the values u200bu200bof c and d, it is possible to define when, how, why and how much is the difference between the result of two equations in which two different mathematical operations operate: addition and multiplication.