**Seventh-Degree Polynomials:** Solve 7th degree equation using algebraic (variant: continuous) functions of two parameters.

Hilbert’s 13th problem is about equations of the form *x ^{7} + ax^{3} + bx^{2} + cx + 1 = 0*. He asked whether solutions to these functions can be written as the composition of finitely many two-variable functions. (Hilbert believed they could not be.) In 1957, Andrey Kolmogorov and Vladimir Arnold proved that each continuous function of

*n*variables — including the case in which

*n = 7*— can be written as a composition of continuous functions of two variables. However, if stricter conditions than mere continuity are imposed on the functions, the question is still open.