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Prime proof zeros in on crucial numbers

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8:00pm, October 18, 2004

Fermat's last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat's tantalizing conjecture.

Now, Preda Mihailescu of the Swiss Federal Institute of Technology in Zurich has proved a theorem that is likely to lead to a solution of Catalan's conjecture, another venerable problem involving relationships among whole numbers. He describes his result in a paper to be published in the Journal of Number Theory.

"This is a very important contribution," says mathematician Andrew Granville of the University of Georgia in Athens. Mihailescu's work probably puts the resolution of Catalan's problem into the foreseeable future, he notes.

Named for Belgian mathematician Eugène Charles Catalan, the conjecture concerns powers of whole numbers. For example, the sequence of all squares and cubes of whole numbers greater than 1 begins with the integers 4, 8,

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