Now, when the general form for the doubly differentiated case is obtained, it is necessary to return to the primordial ones, because this is the identity, resulting in the following equalities (15—16).

And indeed, this value is close to the most potential value, so this expression can be considered the second kind of writing of the exponential unit. Now, it is possible to proceed to the solution of the Euler equation for the general form of the intentional numbers, having carried out the first substitution and the usual replacement operations at stage (17) and (18) at the beginning.

When the necessary transformations come to an end, and other actions no longer take place, it is also sufficient to differentiate both parts of equality as a valid identity (19).

Differentiating the first part of the equality, we can come to the result in (20), and for the second part, the calculations will continue throughout (21).

Then, applying (22—25), one can come to the form (26).

As a result, it is enough to equalize both results in (20) and (26), since these are two parts of the identity, and then get (27) with the necessary simplification, and already in (28) with additional simplification and differentiation as an identity.

At the same time, the differentiation of the first part of equality is obvious in (29), as well as the second in (30), after which equality and the resulting transformations can be introduced into (31).

As a result, equalities are formed that need to be integrated twice, because their derivatives were taken earlier, getting (32).

Integrating the first part, a separate result is obtained in (33) and integrating the second part in (34).

Thus, it is possible to arrive at equality (35), from where it is possible to arrive at another equality in the same equation.

The result is really quite surprising, but this is equality (35), which came out after substituting the general form of an ingential number into Euler’s formula and the solution for this case is the ingential number (36). Thus, this is the first full-fledged equation, the solution of which was an intentional number.

Although the complex numbers themselves are located on the axis of numbers, this interval can also be expressed on the tangential plane. This coordinate system has an axis starting from infinity as the ordinate, and the abscissa has all real numbers. Thus, all exponential numbers can be represented on such a rectangular coordinate system, in the case of adding complex numbers – already in space.

1. I. V. Bargatin, B. A. Grishanin, V. N. Zadkov. Entangled quantum states of atomic systems. Editorial office named after Lomonosov. 2001.

2. G. Kane. Modern elementary particle physics. Publishing house Mir. 1990.

3. S. Hawking. The theory of everything. From singularity to infinity: the origin and fate of the universe. Publishing house AST. 2006.

4. S. Hawking, L. Mlodinov. The supreme plan. A physicist's view of the creation of the world. Publishing house AST. 2010.

5. T. D'amour. The world according to Einstein. From relativity theory to string theory. Moscow Publishing House. 2016.

6. S. Hawking, L. Mlodinov. The shortest history of time. Amphora Publishing House. 2011.

Аннотация. Когда об этой задаче рассказывают молодым математикам – их сразу предупреждают, что не стоит браться за её решение, ибо это кажется невозможным. Простую на вид гипотезу не смогли доказать лучшие умы человечества. Для сравнения, знаменитый математик Пол Эрдеш сказал: «Математика ещё не созрела для таких вопросов». Однако, стоит подробнее изучить данную гипотезу, что и исследуется в настоящей работе.