Assuming Waldschmidt 1973: if e^{ir/π} is algebraic for a rational r ≠ 0, then two of π, e, e^{π²} are algebraically independent

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Assuming Waldschmidt 1973: if e^{ir/π} is algebraic for a rational r ≠ 0, then two of π, e, e^{π²} are algebraically independent · Prove2Me