Let α_i and A_i be algebraic numbers such that the A_is differ from zero and the α_is differ from each other. Then the expression A_1 e^(α_1) + A_2 e^(α_2) + A_3 e^(α_3) + ... cannot equal zero. The theorem was proved by Hermite in the special case of the A_is and α_is rational integers, and subsequently proved for algebraic numbers by Lindemann in 1882. The proof was subsequently simplified by Weierstrass and Gordan.

algebraic number | constant problem | four exponentials conjecture | integer relation | Lindemann-Weierstrass theorem | six exponentials theorem

Charles Hermite | Ferdinand von Lindemann