= Four exponentials conjecture
The <four exponentials conjecture> asserts that if $x_1,x_2$ are <complex numbers> <linearly independent> over $\mathbb Q$, and $y_1,y_2$ are likewise <linearly independent> over $\mathbb Q$, then at least one of the four numbers $e^{x_iy_j}$ is a <transcendental number>.
Both independence hypotheses are essential to the statement. It is a problem in <transcendental number theory>, asking how a two-by-two array of products constrains exponentiation. The analogous statement with two independent $x_i$ and three independent $y_j$ is the <six exponentials theorem>; that stronger supply of inputs is known to force at least one transcendental output. The four-number assertion is a conjecture, not a consequence of checking individual exponentials.
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