Preda Mihăilescu

Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren

The diagonal case of the Nagell-Ljunggren equation is

Current Challenges for IT Security with Focus on Biometry

\frac{{x^p - 1}} {{x - 1}} = p^e \cdot y^p with x,y \in \mathbb{Z} e \in \left\{ {0,1} \right\},

Turning Washington’s Heuristics in Favor of Vandiver’s Conjecture

(1) and p an odd prime. The only known nontrivial solution is

On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation

\frac{{18^3 - 1}} {{18 - 1}} = 7^3 ,

Fingerprint Classification using Entropy Sensitive Tracing

(2) and it is conjectured to be also the only such solution. However, it is not even proved that (1) has only finitely many solution.

Current challenges for biometric security, with focus on fingerprints

We survey approaches to solving the generalized Fermat equation