Sobre la solución a un problema pendiente: no existe un compuesto c que satisfaga la ecuación 2^(c-1)≡1 (mod c^2 )

In this article, a study is made of the possible solutions of the equation 2^(c-1)≡1 (mod c^2 ) to determine that only odd composite numbers can be possible solutions. Then, c=2k+1 is assumed to arrive at expressions of the type 〖 4〗^k-1 and through the study from k=1 to k=70 and the insertion into the number theory of the concept of “codependent primes of the exponent k”, of which programs and examples are shown, as well as characteristics of its use, mathematical arguments are reached that show the nonexistence of any composite number that satisfies the indicated equation. Throughout the article, the relationship between the prime factors and the exponents is made, explanatory tables and arguments of the exponents and the possible divisors (prime factors) are presented to conclude that the existence of solutions is impossible.