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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  (7)
PAJAZITI, Antigona  (3)
BENOIST, Alexandre  (2)
Main Referenced Keywords
Kummer theory (8); Degree (4); number field (3); Number fields (3); degree (2);
Main Referenced Disciplines
Mathematics (129)
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others (6)
Arts & humanities: Multidisciplinary, general & others (4)
Languages & linguistics (2)
Education & instruction (2)

Publications (total 145)

The most downloaded
902 downloads
PERUCCA, A. (2021). The Hardest Logic Puzzle Ever. Plus Magazine. https://hdl.handle.net/10993/43876

The most cited

21 citations (OpenAlex)

PERUCCA, A. (2018). Reductions of algebraic integers II. Association for Women in Mathematics Series. doi:10.1016/j.jnt.2016.03.001 https://hdl.handle.net/10993/34416

The most significant

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

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. (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


PERUCCA, A., SAGMAN, N., & Verfaillie, G. (In press). Congruence theorems for triangles and convex quadrilaterals involving heights. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/61451.

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

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

BENOIST, A., & PERUCCA, A. (2025). Two variants of the Lang-Trotter conjecture on primitive points for elliptic curves. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/64259.

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

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

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

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., & 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). 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. (2024). Number theorist mug.

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

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

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

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). The decimal representation of a fraction. Uitwiskeling.

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

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

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

PERUCCA, A. (2023). Horizontal.

PERUCCA, A. (2023). BIGsmall.

PERUCCA, A. (2023). BIG.

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. (2022). Visual Mathematical Dictionary.

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

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). Minorities in Mathematics. MaddMaths!.

PERUCCA, A. (2022). Silent Danger.

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

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

PERUCCA, A. (2021). Staircase numbers. 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

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). The Hardest Logic Puzzle Ever. Plus Magazine.

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

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., & 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.

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

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.

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. doi:10.1142/S179304211950091X
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. (2020). The degree of non-Galois Kummer extensions of number fields. Rivista di Matematica della Universita di Parma, 11, 301-313.
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

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

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

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

PERUCCA, A., & STRANEN, D. (2019). Trigonometry for the multiples of 3 degrees. 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. (2018). Arithmetic Billiards. Plus Magazine, University of Cambridge.

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

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. doi:10.1142/S1793042117500828
Peer reviewed

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

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

PERUCCA, A. (2017). The Chinese Remainder Clock. College Mathematics Journal. doi:10.4169/college.math.j.48.2.82
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). Reductions of one-dimensional tori. International Journal of Number Theory. doi:10.1142/S1793042117500828
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 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.). 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.

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

PERUCCA, A. (n.d.). Congruence theorems for triangles involving medians and bisectors. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55781.

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

BARIL BOUDREAU, F., & PERUCCA, A. (n.d.). Kummer theory for function fields. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/61493.

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

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

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

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

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

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

PERUCCA, A. (n.d.). Associativity versus Commutativity.

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

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

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

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

PERUCCA, A., & Tholl, M. (n.d.). Computing primitive roots according to Artin's conjecture. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/60102.

PERUCCA, A. (n.d.). A didactical reflection on varying quantities.

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

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

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

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

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

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

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

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

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.). Four Riddles with Four Brothers. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/44573.

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

PERISSINOTTO, F., & PERUCCA, A. (n.d.). Kummer theory for p-adic fields. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/50285.

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

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

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.). Saddle point walk.

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

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

Olli Järviniemi, PERUCCA, A., & Pietro Sgobba. (n.d.). Unified treatment of Artin-type problems II. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52916.

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.). Pascal triangle for kids. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/52597.

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.). Art and Data Science: a model by pupils.

Moree, P., PERUCCA, A., & SGOBBA, P. (n.d.). The distribution of the multiplicative index of algebraic numbers over residue classes. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/54490.

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

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

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

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

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

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

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

Benoist, A., & PERUCCA, A. (n.d.). The ternary cyclotomic polynomials Φ_3pq. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55534.

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

ADVOCAAT, B., CHAN, C. W., PAJAZITI, A., PERISSINOTTO, F., & PERUCCA, A. (n.d.). Galois groups of Kummer extensions of number fields. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55190.

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

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

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

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