Mersenne version of Brocard-Ramanujan equation

In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one interesting and still open problems Diophantine analysis. We search for positive integer solutions equation case where right-hand side Mersenne numbers. By using definition numbers, appropriate inequalities parameters prime factorization $n!$ show that there no solution to equation. Thus, obtain result demonstrating square any number can not be expressed as $n!+1$.