Back
  1. Home
  2. Profile of Antonella PERUCCA (Unilu)
Profil

PERUCCA Antonella

University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)

ORCID
0000-0003-3173-6988
Main Referenced Co-authors
SGOBBA, Pietro  (10)
TRONTO, Sebastiano  (9)
PERISSINOTTO, Flavio  (6)
BENOIST, Alexandre  (4)
PAJAZITI, Antigona  (3)
Main Referenced Keywords
Kummer theory (8); Degree (4); number field (3); Number fields (3); degree (2);
Main Referenced Disciplines
Mathematics (143)
Arts & humanities: Multidisciplinary, general & others (6)
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others (6)
Languages & linguistics (2)
Education & instruction (2)

Publications (total 161)

The most downloaded
3054 downloads
PERUCCA, A., & TORTI, E. (2023). Congruence theorems for convex polygons involving sides, angles, and diagonals. International Journal of Geometry, 12 (2023), 83-92. https://hdl.handle.net/10993/46631

The most cited

22 citations (OpenAlex)

Debry, C., & PERUCCA, A. (2016). Reductions of algebraic integers. Journal of Number Theory. doi:10.1016/j.jnt.2016.03.001 https://hdl.handle.net/10993/34412

The most significant

GROTTO, F., PERUCCA, A., & Van Steenbergen Bergeron, T. (2024). Rubik's Snakes on a plane. College Mathematics Journal. doi:10.1080/07468342.2023.2293416
Peer Reviewed verified by ORBi

PERUCCA, A., SEURÉ, T., & WOLFF, V. (2024). Divisibility Graphs and Modular Multiplication Tables. American Mathematical Monthly. doi:10.1080/00029890.2023.2298181
Peer Reviewed verified by ORBi

PERUCCA, A. (2023). Congruence Theorems in the past, present, and future. For the Learning of Mathematics.
Peer reviewed

Olli Järviniemi, & PERUCCA, A. (2022). Unified treatment of Artin-type problems. Research in Number Theory. doi:10.1007/s40993-022-00418-6
Peer Reviewed verified by ORBi

Lombardo, D., & PERUCCA, A. (2019). Reductions of points on algebraic groups. Journal of the Institute of Mathematics of Jussieu. doi:10.1017/S1474748019000598
Peer reviewed


BENOIST, A., & PERUCCA, A. (2026). Two variants of the Lang-Trotter conjecture on primitive points for elliptic curves. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/64259.

Benoist, A., & PERUCCA, A. (2026). The ternary cyclotomic polynomials Φ_3pq. Involve: a Journal of Mathematics, 19 (1), 51-72.
Peer reviewed

PERISSINOTTO, F., & PERUCCA, A. (2026). Kummer theory for p-adic fields. Functiones et Approximatio, Commentarii Mathematici.
Peer reviewed

PERUCCA, A. (2026). Geometrical cake cutting. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2026). A probability riddle about finding the fève in the galette des rois.

ADVOCAAT, B., CHAN, C. W., PAJAZITI, A., PERISSINOTTO, F., & PERUCCA, A. (2025). Galois groups of Kummer extensions of number fields. Publ. Mathématiques de Besançon.
Peer reviewed

PERIC, M., & PERUCCA, A. (2025). Mathematics in the Vichten Roman Mosaic. Journal of Humanistic Mathematics. doi:10.5642/jhummath.HGPD5677
Peer Reviewed verified by ORBi

Olli Järviniemi, PERUCCA, A., & Pietro Sgobba. (2025). Unified treatment of Artin-type problems II. Research in Number Theory. doi:10.1007/s40993-025-00620-2
Peer Reviewed verified by ORBi

PERUCCA, A. (2025). Math CEO (of AI).

Giacomo Cherubini, & PERUCCA, A. (2025). On the vanishing of the density in Artin's conjecture on primitive roots. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/65032.

PERUCCA, A. (2025). Friendly mathematical exercises.

PERUCCA, A., SAGMAN, N., & Verfaillie, G. (2025). Congruence theorems for triangles and convex quadrilaterals involving heights. International Electronic Journal of Geometry.
Peer reviewed

BARIL BOUDREAU, F., & PERUCCA, A. (2025). Kummer theory for function fields. Journal of Number Theory. doi:10.1016/j.jnt.2025.01.004
Peer Reviewed verified by ORBi

Fité, F., & PERUCCA, A. (2024). A local-global principle for polyquadratic twists of abelian surfaces. Indiana University Mathematics Journal. doi:10.1512/iumj.2024.73.60110
Peer Reviewed verified by ORBi

PERUCCA, A. (2024). Number theorist mug.

PERUCCA, A. (2024). Interpreting sets of natural numbers as real numbers.

GROTTO, F., PERUCCA, A., & Van Steenbergen Bergeron, T. (2024). Rubik's Snakes on a plane. College Mathematics Journal. doi:10.1080/07468342.2023.2293416
Peer Reviewed verified by ORBi

PERUCCA, A. (2024). SuperPLUS Poster.

PERISSINOTTO, F., & PERUCCA, A. (2024). Kummer extensions of finite fields. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/61215.

PERUCCA, A. (2024). Cardinalities and the continuum hypothesis. Uitwiskeling.
Editorial reviewed

PERUCCA, A., & Nesterenko, O. (2024). Numeral coins for numeral systems. In Beiträge zum Mathematikunterricht (Tagungsband GDM) (2024). WTM-Verlag Münster.

PERUCCA, A., & Tholl, M. (2024). Computing primitive roots according to Artin's conjecture. JP Journal of Algebra, Number Theory and Applications. doi:10.17654/0972555524026
Peer reviewed

PERUCCA, A. (2024). The decimal representation of a fraction. Uitwiskeling.
Editorial reviewed

PERUCCA, A., & Sgobba, P. (2024). Comparing densities for powers in Artin's conjecture on primitive roots. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/59821.

Moree, P., PERUCCA, A., & SGOBBA, P. (2024). The distribution of the multiplicative index of algebraic numbers over residue classes. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. doi:10.1007/s12188-024-00276-2
Peer Reviewed verified by ORBi

PERUCCA, A., & Shparlinski, I. (2024). Uniform bounds for the density in Artin's conjecture on primitive roots. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/59696.

PERUCCA, A. (2024). Advertisement for mathematical competitions.

PERUCCA, A., SEURÉ, T., & WOLFF, V. (2024). Divisibility Graphs and Modular Multiplication Tables. American Mathematical Monthly. doi:10.1080/00029890.2023.2298181
Peer Reviewed verified by ORBi

PAJAZITI, A., & PERUCCA, A. (2024). One formal result for torsion and arboreal representations of commutative algebraic groups. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/61266.

Kasel, T., & PERUCCA, A. (2024). Primitive roots and 6-Germain primes. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/61320.

PERUCCA, A. (2024). Didactics without borders.

PERISSINOTTO, F., & PERUCCA, A. (2023). Kummer theory for products of one-dimensional tori. Publications Mathematiques de Besançon, 2023, 109-119. doi:10.5802/pmb.51
Peer reviewed

PERUCCA, A. (2023). Multiplying mathematical teachers.

PERUCCA, A. (2023). Soft skills for mathematical teachers.

PERUCCA, A. (2023). Congruence Theorems in the past, present, and future. For the Learning of Mathematics.
Peer reviewed

PERUCCA, A., & TORTI, E. (2023). Congruence theorems for convex polygons involving sides, angles, and diagonals. International Journal of Geometry, 12 (2023), 83-92.
Peer reviewed

PERUCCA, A. (2023). BIGsmall.

PERUCCA, A. (2023). BIG.

PERUCCA, A. (2023). Horizontal.

PERUCCA, A. (2022). Silent Danger.

PERUCCA, A., Reguengo da Sousa, J., & TRONTO, S. (2022). Arithmetic Billiards. Recreational Mathematics Magazine.
Peer reviewed

Hoermann, F., PERUCCA, A., SGOBBA, P., & TRONTO, S. (2022). Explicit Kummer generators for cyclotomic extensions. JP Journal of Algebra, Number Theory and Applications. doi:10.17654/0972555522004
Peer reviewed

PERUCCA, A. (2022). Minorities in Mathematics. MaddMaths!.

Olli Järviniemi, & PERUCCA, A. (2022). Unified treatment of Artin-type problems. Research in Number Theory. doi:10.1007/s40993-022-00418-6
Peer Reviewed verified by ORBi

FOYEN, A., & PERUCCA, A. (2022). Der 50cm lange Gliedermaßstab. In Beiträge zum Mathematikunterricht 2022 (Tagungsband GDM).

Andrusiak, R., & PERUCCA, A. (2022). Sharing calculations to understand arithmetical algorithms and parallel computing. Mathematics Teacher.
Peer Reviewed verified by ORBi

PERUCCA, A. (2022). Visual Mathematical Dictionary.

PERISSINOTTO, F., & PERUCCA, A. (2022). Kummer theory for multiquadratic or quartic cyclic number fields. Uniform distribution theory, 17 (no. 2), 165-194.
Peer reviewed

PERUCCA, A., & RONK, P. F. (2022). Proportionalitätsrechner für Menschen mit einer Dyskalkulie [Paper presentation]. GDM Meeting 2022, Frankfurt, Germany.

PERUCCA, A. (2022). Geometrie der römischen Mosaiken [Paper presentation]. GDM Meeting 2022.

PERUCCA, A., & TRONTO, S. (2021). How to become the world record holder for solving the Rubik's cube.

PERUCCA, A. (2021). The Hardest Logic Puzzle Ever. Plus Magazine.

PERUCCA, A., SGOBBA, P., & TRONTO, S. (2021). The degree of Kummer extensions of number fields. International Journal of Number Theory. doi:10.1142/S1793042121500263
Peer Reviewed verified by ORBi

Hörmann, F., PERUCCA, A., SGOBBA, P., & TRONTO, S. (2021). Explicit Kummer theory for quadratic fields. JP Journal of Algebra, Number Theory and Applications. doi:10.17654/NT050020151
Peer reviewed

PERUCCA, A., SGOBBA, P., & TRONTO, S. (2021). Kummer theory for number fields via entanglement groups. Manuscripta Mathematica. doi:10.1007/s00229-021-01328-0
Peer Reviewed verified by ORBi

PERUCCA, A. (2021). Every number is the beginning of a power of 2. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2021). Staircase numbers. Uitwiskeling.
Editorial reviewed

PERUCCA, A., SGOBBA, P., & TRONTO, S. (2020). Kummer theory for number fields. Proceedings of the Roman Number Theory Association.

PERUCCA, A., & Todorovic, M. (2020). Visualizations for the Principle of Mathematical Induction. In Beiträge zum Mathematikunterricht 2020. Münster, Germany: WTM-Verlag.

PERUCCA, A., SGOBBA, P., & TRONTO, S. (2020). Explicit Kummer theory for the rational numbers. International Journal of Number Theory. doi:10.1142/S1793042120501146
Peer Reviewed verified by ORBi

PERUCCA, A., & SGOBBA, P. (2020). Kummer theory for number fields and the reductions of algebraic numbers II. Uniform distribution theory.
Peer reviewed

Bruin, P., & PERUCCA, A. (2020). Reductions of points on algebraic groups II. Glasgow Mathematical Journal. doi:10.1017/S0017089520000336
Peer Reviewed verified by ORBi

PERUCCA, A., & STRANEN, D. (2020). Converting the Old Babylonian Tablet ‘Plimpton 322’ into the Decimal System as a Classroom Exercise. Convergence.
Peer Reviewed verified by ORBi

BEGALLA, E., & PERUCCA, A. (2020). The ABCD of cyclic quadrilaterals. Uitwiskeling.
Editorial reviewed

PERUCCA, A., SGOBBA, P., & TRONTO, S. (2020). Addendum to: Reductions of algebraic integers. Journal of Number Theory. doi:10.1016/j.jnt.2016.09.004
Peer Reviewed verified by ORBi

Carvalho da Veiga, B., & PERUCCA, A. (2020). Arithmetic billiards in dimension n. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/62134.

PERUCCA, A. (2020). The seven bridges of Königsberg. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2020). Four points, two distances. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2020). The 15 puzzle. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2020). The degree of non-Galois Kummer extensions of number fields. Rivista di Matematica della Universita di Parma, 11, 301-313.
Peer reviewed

PERUCCA, A. (2019). Multisets in arithmetics. In Multimengen in der Arithmetik. Münster, Germany: WTM-Verlag.

Lombardo, D., & PERUCCA, A. (2019). Reductions of points on algebraic groups. Journal of the Institute of Mathematics of Jussieu. doi:10.1017/S1474748019000598
Peer reviewed

PERUCCA, A. (2019). Multiplicative order and Frobenius symbol for the reductions of number fields. Research Directions in Number Theory, Association for Women in Mathematics, Series 19 (2019).
Peer reviewed

PERUCCA, A., & SGOBBA, P. (2019). Kummer theory for number fields and the reductions of algebraic numbers. International Journal of Number Theory. doi:10.1142/S179304211950091X
Peer Reviewed verified by ORBi

PERUCCA, A. (2019). Reductions of elliptic curves. Proceedings of the Roman Number Theory Association, 4.

PERUCCA, A. (2019). The problem of detecting linear dependence. Rivista di Matematica della Universita di Parma.
Peer reviewed

PERUCCA, A., & STRANEN, D. (2019). Trigonometry for the multiples of 3 degrees. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2019). Multisets. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2019). The Art Gallery Problem. Uitwiskeling, 35 (3).
Editorial reviewed

PERUCCA, A. (2018). Reductions of algebraic integers II. Association for Women in Mathematics Series. doi:10.1016/j.jnt.2016.03.001
Peer reviewed

PERUCCA, A. (2018). Reductions of one-dimensional tori II. Association for Women in Mathematics Series.
Peer reviewed

PERUCCA, A. (2018). The PytEuk puzzle.

PERUCCA, A. (2018). Math around the Clock. Plus Magazine, University of Cambridge.

PERUCCA, A., Fiore, T., & Lang, A. (2018). Tactile Tools for Teaching: Implementing Knuth's Algorithm for Mastering Mastermind. College Mathematics Journal.
Peer Reviewed verified by ORBi

PERUCCA, A. (2018). Arithmetic Billiards. Plus Magazine, University of Cambridge.

PERUCCA, A., & Van den Broek, L. (2018). Driehoeken met onderling 5 gelijke zijden en hoeken. Uitwiskeling.
Editorial reviewed

PERUCCA, A. (2017). Reductions of one-dimensional tori. International Journal of Number Theory. doi:10.1142/S1793042117500828
Peer Reviewed verified by ORBi

Lombardo, D., & PERUCCA, A. (2017). The 1-eigenspace for matrices in GL2(ℤℓ). New York Journal of Mathematics.
Peer reviewed

PERUCCA, A. (2017). The Chinese Remainder Clock. College Mathematics Journal. doi:10.4169/college.math.j.48.2.82
Peer Reviewed verified by ORBi

Debry, C., & PERUCCA, A. (2016). Reductions of algebraic integers. Journal of Number Theory. doi:10.1016/j.jnt.2016.03.001
Peer Reviewed verified by ORBi

PERUCCA, A. (2015). The order of the reductions of an algebraic integer. Journal of Number Theory. doi:10.1016/j.jnt.2014.09.022
Peer reviewed

PERUCCA, A. (2015). The prime divisors of the number of points on abelian varieties. Journal de Théorie des Nombres de Bordeaux. doi:10.5802/jtnb.924
Peer reviewed

PERUCCA, A. (n.d.). Hexoku and other Sudoku variants.

PERUCCA, A. (n.d.). MATHS CALENDAR (12 language inclusive posters).

MEYRATH, T., Mincu, C.-I., & PERUCCA, A. (n.d.). Training mathematical thinking with the inclusive card game UNO.

PERUCCA, A. (n.d.). Math in Disguise: Constructing Braids.

PERUCCA, A. (n.d.). Saddle point walk.

PERUCCA, A. (n.d.). Role models for minorities in mathematics.

PERUCCA, A. (n.d.). Rubik's Snakes: Learn and Play. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52977.

PERUCCA, A. (n.d.). TikZ is more than meets the eyes. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/53003.

BENOIST, A., Johanna Hoffmann, PERUCCA, A., & Lucile Turquin. (n.d.). Choosing the movie for a movie night.

PERUCCA, A. (n.d.). Mathematical Competencies.

PERUCCA, A. (n.d.). A significant error in number recognition due to multilingualism.

PERUCCA, A., & Sanna Carlo. (n.d.). On candidates to be primitive roots. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/67069.

PERUCCA, A. (n.d.). Didaktik der Geometrie im 21. Jahrhundert. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/67195.

PERUCCA, A., & RONK, P. F. (n.d.). Beware proportions. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/51229.

PERUCCA, A. (n.d.). Fermat's Last Theorem (Worksheet for pupils).

Steve Mendeleev, Flavio Perissinotto, & PERUCCA, A. (n.d.). Three-dimensional arithmetic billiards. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/47098.

PERUCCA, A. (n.d.). Reflections on milestones in pre-school mathematics.

PERUCCA, A. (n.d.). Creativity Backstage.

NESTERENKO, O., & PERUCCA, A. (n.d.). Challenging variants of the “Guess who?” game.

PERUCCA, A. (n.d.). Mathematical hourglasses, just in time. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52537.

PERUCCA, A. (n.d.). Pascal triangle for kids. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52597.

PERUCCA, A. (n.d.). Four Riddles with Four Brothers. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/44573.

PERUCCA, A. (n.d.). The least common multiple of several numbers in terms of greatest common divisors. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/44718.

PERUCCA, A. (n.d.). Boy or Girl? ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/45294.

PERUCCA, A. (n.d.). The first-digit law. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/45191.

PERUCCA, A. (n.d.). MatheMAGICAL: Flow rings.

PERUCCA, A. (n.d.). MatheMAGICAL: Guess the number.

Fabio Génin, & PERUCCA, A. (n.d.). SageMath for teachers.

PERUCCA, A. (n.d.). Funnier arithmetic sequences.

PERUCCA, A. (n.d.). Mathematical Escape Game Sample Riddle.

PERUCCA, A. (n.d.). Math in disguise.

Paul Deutsch, Leal Cordeiro, D., & PERUCCA, A. (n.d.). The Wallet Problem.

BENOIST, A., Costa, A., Hinger, C., Hoffmann, J., PERUCCA, A., & Turquin, L. (n.d.). Mathematics for voting.

PERUCCA, A. (n.d.). Is it truly possible to vary quantities?

PERUCCA, A. (n.d.). Ceci n'est pas un carré.

PERUCCA, A. (n.d.). Data Science Stories.

PERUCCA, A. (n.d.). Fuzzy true/false quiz.

PERUCCA, A. (n.d.). Those new mistakes (minority focus).

PERUCCA, A. (n.d.). Generalized associativity.

PERUCCA, A. (n.d.). Quadratic equations: from trivial to impossible.

PERUCCA, A. (n.d.). Exponentiation as a complex operation.

PERUCCA, A. (n.d.). Imaginary Ghosts.

PERUCCA, A. (n.d.). The improbable outcome.

PERUCCA, A. (n.d.). Comics for learning.

PERUCCA, A. (n.d.). Addition walls. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55772.

Jie Chen, Filipa Gonçalves Marques, MARTINEZ GRANADO, D., PERUCCA, A., & Sanny Schwartz. (n.d.). Congruence theorems for triangles involving angle bisectors. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55781.

PERUCCA, A. (n.d.). Art and Data Science: a model by pupils.

PERUCCA, A. (n.d.). Multilingual tuning of ABC posters.

PERUCCA, A. (n.d.). Kummer extensions of number fields (the case of rank 2). ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/41552.

PERUCCA, A. (n.d.). Unconscious assumptions in mathematical examples. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/50582.

PERUCCA, A. (n.d.). One dog, one cat, one mouse (mathematical exhibit).

PERUCCA, A. (n.d.). The Multiplication Tables Puzzle.

PERUCCA, A. (n.d.). Junior BINGO. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/51614.

PERUCCA, A. (n.d.). Linear relations among radicals. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/66217.

PERUCCA, A. (n.d.). Save Wikipedia for mathematics education.

PERUCCA, A. (n.d.). A closed formula for the density in Artin's primitive root conjecture over number fields. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/66409.

BENOIST, A., BUZOGANY, S., & PERUCCA, A. (n.d.). On the independence of divisibility conditions for elliptic curves. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/66966.

PERUCCA, A. (n.d.). Birthday Presents Math. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/62272.

PERUCCA, A. (n.d.). Funny geometrical fact: equilateral triangles inscribed in squares. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/62269.

CHAN, C. W., PAJAZITI, A., PERISSINOTTO, F., & PERUCCA, A. (n.d.). On the entanglement of radicals. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/62415.

PERUCCA, A. (n.d.). SOS Sudoku. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/43835.

PERUCCA, A. (n.d.). The one key element for undergraduate research is.

PERUCCA, A. (n.d.). Choosing Female Role Models in Mathematics.

PERUCCA, A. (n.d.). For the sake of mathematics.

GRUETZNER, G., PERUCCA, A., Seny, F., & Thalmeier, T. (n.d.). Congruence theorems for trapezoids. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/68298.

PERUCCA, A. (n.d.). From Snow White to mathematical stories.

BUZOGANY, S., & PERUCCA, A. (n.d.). The group GL_2(Z/nZ) as permutations of (Z/nZ)^2. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/67597.

PERUCCA, A. (n.d.). What is the capital of France?

PERUCCA, A. (n.d.). Teachers' emergencies.

Contact ORBilu