A mathematician at the University of Debrecen has solved a long-standing problem in number theory originally posed decades ago. The research focused on Diophantine equations—equations seeking integer solutions—and examined a generalized form of the equation involving exponential powers.The study proved that for any three relatively prime integers greater than one, the equation has at most two positive integer solutions, with only two specific exceptional cases yielding three solutions. The 78-page proof underwent a two-year review process before being published in the prestigious American Journal of Mathematics and received international recognition, including a major academic publication award.Although classified as fundamental research, the findings contribute to number theory, which underpins modern digital security systems such as encryption and secure financial transactions. The breakthrough provides new mathematical methods that could influence future technological foundations.
Source: University of Debrecen
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