History
A special case of the result where x1, x2, and x3 are logarithms of positive integers, y1 = 1, and y2 is real, was first mentioned in a paper by Leonidas Alaoglu and Paul Erdős from 1944 in which they try to prove that the ratio of consecutive colossally abundant numbers is always prime. They claimed that Carl Ludwig Siegel knew of a proof of this special case, but it is not recorded. Using the special case they manage to prove that the ratio of consecutive colossally abundant numbers is always either a prime or a semiprime.
The theorem was first explicitly stated and proved in its complete form independently by Serge Lang and Kanakanahalli Ramachandra in the 1960s.
Read more about this topic: Six Exponentials Theorem
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