Six Exponentials Theorem - History

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

Famous quotes containing the word history:

    History ... is, indeed, little more than the register of the crimes, follies, and misfortunes of mankind.
    But what experience and history teach is this—that peoples and governments have never learned anything from history, or acted on principles deduced from it.
    Georg Wilhelm Friedrich Hegel (1770–1831)

    The history of all hitherto existing society is the history of class struggles.
    Karl Marx (1818–1883)

    History does nothing; it does not possess immense riches, it does not fight battles. It is men, real, living, who do all this.... It is not “history” which uses men as a means of achieving—as if it were an individual person—its own ends. History is nothing but the activity of men in pursuit of their ends.
    Karl Marx (1818–1883)