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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 (141)
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others (6)
Arts & humanities: Multidisciplinary, general & others (5)
Languages & linguistics (2)
Education & instruction (2)

Publications (total 158)

The most downloaded
3002 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.

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.

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

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

Olli Järviniemi, PERUCCA, A., & Pietro Sgobba. (2025). Unified treatment of Artin-type problems II. Research in Number Theory.
Peer Reviewed verified by ORBi

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

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). Math CEO (of AI).

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

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

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

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

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

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

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). The decimal representation of a fraction. Uitwiskeling.

PERUCCA, A. (2024). SuperPLUS Poster.

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

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

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

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

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.

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.

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.

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

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

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

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., & 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). Horizontal.

PERUCCA, A. (2023). BIGsmall.

PERUCCA, A. (2023). BIG.

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

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

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

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

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

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

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). Silent Danger.

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

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. (2021). Every number is the beginning of a power of 2. Uitwiskeling.

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). Staircase numbers. Uitwiskeling.

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

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., 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

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

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

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. (2020). The seven bridges of Königsberg. Uitwiskeling.

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

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

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). Kummer theory for number fields. Proceedings of the Roman Number Theory Association.

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

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

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

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

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

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

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

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

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

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 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. (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. (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.). SOS Sudoku. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/43835.

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.). Fermat's Last Theorem (Worksheet for pupils).

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.). 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.). Creativity Backstage.

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

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.). A significant error in number recognition due to multilingualism.

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

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

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.). Reflections on milestones in pre-school mathematics.

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

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.

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

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

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

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

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

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

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

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.). A probability riddle about finding the fève in the galette des rois.

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

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.

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

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.). Generalized associativity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.). The one key element for undergraduate research is.

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.

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

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