Let (x_1, x_2) and (y_1, y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of e^(x_1 y_1), e^(x_1 y_2), e^(x_2 y_1), e^(x_2 y_2) is transcendental (Waldschmidt 1979, p. 3.5). The corresponding statement obtained by replacing y_1, y_2 with y_1, y_2, y_3 has been proven and is known as the six exponentials theorem.

Hermite-Lindemann theorem | six exponentials theorem | transcendental number