 The six exponentials theorem then follows by setting β"ij" = 0 for every "i" and "j", while the five exponentials theorem follows by setting "x"3 = γ/"x"1 and using Baker's theorem to ensure that the "x""i" are linearly independent.There is a sharp version of the five exponentials theorem as well, although it as yet unproven so is known as the sharp five exponentials conjecture.This conjecture implies both the sharp six exponentials theorem and the five exponentials theorem, and is stated as follows.