# Preda Mihăilescu

#11,637

Most Influential Person Now

Mathematician

## Preda Mihăilescu's AcademicInfluence.com Rankings

Preda Mihăilescumathematics Degrees

Mathematics

#929

World Rank

#1624

Historical Rank

Measure Theory

#4955

World Rank

#5831

Historical Rank

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Mathematics

## Preda Mihăilescu's Degrees

- PhD Mathematics University of Göttingen

## Why Is Preda Mihăilescu Influential?

(Suggest an Edit or Addition)According to Wikipedia, Preda V. Mihăilescu is a Romanian mathematician, best known for his proof of the 158-year-old Catalan's conjecture. Biography Born in Bucharest, he is the brother of Vintilă Mihăilescu. After leaving Romania in 1973, he settled in Switzerland. He studied mathematics and computer science in Zürich, receiving a PhD from ETH Zürich in 1997. His PhD thesis, titled Cyclotomy of rings and primality testing, was written under the direction of Erwin Engeler and Hendrik Lenstra.

## Preda Mihăilescu's Published Works

### Published Works

- Primary cyclotomic units and a proof of Catalans conjecture (2004) (335)
- The Fuzzy Vault for Fingerprints is Vulnerable to Brute Force Attack (2007) (115)
- Robust Orientation Field Estimation and Extrapolation Using Semilocal Line Sensors (2009) (69)
- Security Considerations in Minutiae-Based Fuzzy Vaults (2015) (66)
- A class number free criterion for catalan's conjecture (2003) (46)
- The Generalized Fermat Equation (2016) (24)
- Fast Generation of Provable Primes Using Search in Arithmetic Progressions (1994) (24)
- Generic Efficient Arithmetic Algorithms for PAFFs (Processor Adequate Finite Fields) and Related Algebraic Structures (Extended Abstract) (2003) (21)
- Cyclotomy Primality Proving - Recent Developments (1998) (21)
- On the Nagell-Ljunggren equation $(x^n - 1)/(x - 1) = y^q$ (2007) (21)
- Computing the eigenvalue in the schoof-elkies-atkin algorithm using abelian lifts (2007) (18)
- Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren (2008) (15)
- On the class groups of cyclotomic extensions in presence of a solution to Catalan's equation (2006) (15)
- Cyclotomy of rings & primality testing (1997) (13)
- Dynamic threshold using polynomial surface regression with application to the binarization of fingerprints (2005) (12)
- Dual Elliptic Primes and Applications to Cyclotomy Primality Proving (2007) (11)
- Improved Fingerprint Image Segmentation and Reconstruction of Low Quality Areas (2010) (10)
- New bounds and conditions for the equation of Nagell–Ljunggren (2007) (9)
- Fast convolutions meet Montgomery (2007) (7)
- Reflection, Bernoulli Numbers and the Proof of Catalan's Conjecture (2005) (7)
- Elliptic Gauss sums and applications to point counting (2010) (6)
- Fingerprint Classification using Entropy Sensitive Tracing (2008) (4)
- Cyclotomy Primality Proofs and their Certificates (2007) (4)
- Robust orientation field estimation in fingerprint images with broken ridge lines (2009) (4)
- Contributions in Analytic and Algebraic Number Theory (2012) (3)
- Security of Biased Sources for Cryptographic Keys (2001) (3)
- Algorithms for Generating, Testing and Proving Primes: A Survey (2001) (3)
- Review of the book "Elliptic Curves in Cryptography" by I. Blake, G. Seroussi, N. Smart. (2001) (3)
- Recent developments in primality proving (1999) (3)
- Improved lower bounds for possible solutions in the Second Case of the Fermat Last Theorem and in the Catalan Equation (2021) (2)
- A Primality Test Using Cyclotomic Extensions (1988) (2)
- Hierarchically linked extended features in fingerprints (2008) (2)
- On Leopoldt's conjecture and some consequences (2009) (2)
- Double exponential lower bounds for possible solutions in the Second Case of the Fermat Last Theorem (2021) (2)
- On the vanishing of Iwasawa's constant $\mu$ for the cyclotomic $\Z_p$-extensions of $CM$ number fields (2014) (1)
- Seminar Notes on Open Questions in Iwasawa Theory - SNOQIT I: The $\Lambda[ G ]$-modules of Iwasawa theory II: Units and Kummer theory in Iwasawa extensions (2010) (1)
- On equation Xn − 1 = BZn (2017) (1)
- The $T$ and $T^*$ components of $\Lambda$ - modules and Leopoldt's conjecture (2009) (1)
- Turning Washington’s Heuristics in Favor of Vandiver’s Conjecture (2012) (1)
- A Cylcotomic Investigation of the Fermat - Catalan Equation (2007) (1)
- Iwasawa's constant $\mu$ vanishes in cyclotomic $\Z_p$-extensions of CM fields (2011) (1)
- Chapter 1 Computational Number Theory and Cryptography ∗ (0)
- Contributions in analytic and algebraic number theory : festschrift for S.J. Patterson (2012) (0)
- Primes and the Beauty of Algorithms (2011) (0)
- On the equation X^n-1=B.Z^n (2014) (0)
- Small Fields with Large Class Groups (2020) (0)
- A Diophantine equation concerning epimoric ratios (2022) (0)
- The Artin Symbol as a Canonical Capitulation Map (2009) (0)
- Leopoldt's Conjecture for CM fields (2011) (0)
- Semilocal approximation for the Fermat-Catalan and further popular Diophantine norm equations (2021) (0)
- Current Challenges for IT Security with Focus on Biometry (2015) (0)
- On Vandiver’s Best Result on FLT1 (2012) (0)
- Conceiving a conjecture, and other stories about Eugène Charles CATALAN (2015) (0)
- On cryptographical protocols and procedures: NTRU and the shortest vector protection (2015) (0)
- On solutions of the equation $X^n+ Y^n=B Z^n$ with prime $n|BZ$ (2009) (0)
- Current challenges for biometric security, with focus on fingerprints (2016) (0)
- SNOQIT I: Growth of $\Lambda$-modules and Kummer theory (2011) (0)
- The Leopoldt and Iwasawa Conjectures for CM fields (2014) (0)
- A Conditional Proof of the Leopoldt Conjecture for CM Fields (2021) (0)
- Greenberg notes for the first time a relation between the Leopoldt Conjecture and a special case of the Greenberg Conjecture : he shows that Leopoldt ’ s Conjecture implies (2009) (0)
- The Gross - Kuz'min conjecture for CM fields (2011) (0)
- Public Key Cryptography, Number Theory and Applications (2013) (0)
- Computational Number Theory and Cryptography (2014) (0)
- The Charm of Units I, On the Kummer–Vandiver Conjecture. Extended Abstract (2020) (0)
- Exercises for the Lecture on Computational Number Theory (2012) (0)
- Applications of Baker Theory to the Conjecture of Leopoldt (2009) (0)

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## What Schools Are Affiliated With Preda Mihăilescu?

Preda Mihăilescu is affiliated with the following schools: