On the exponent of some numerical equations

The article deals with numerical equality with integer, positive, mutually simple bases and natural exponent n > 1. The conditions of fidelity of such numerical equations are found. It is shown that such numerical equations exist when the exponent is equal to the number of terms of equality, and the famous Fermat's large theorem is a special case of the reduced theorem. Since the theorem is proved at a fairly simple level, it is a proof that Fermat was not mistaken and indeed proved his famous theorem.