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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  (5)
Lombardo, Davide (2)
Olli Järviniemi (2)
Main Referenced Keywords
Kummer theory (8); Degree (4); number field (3); Number fields (3); degree (2);
Main Referenced Disciplines
Mathematics (112)
Arts & humanities: Multidisciplinary, general & others (5)
Languages & linguistics (2)
Social & behavioral sciences, psychology: Multidisciplinary, general & others (2)
Business & economic sciences: Multidisciplinary, general & others (1)

Publications (total 125)

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

The most cited

15 citations (OpenCitations)

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

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: Graphs representing modular multiplications. American Mathematical Monthly.
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

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


Fité, F., & Perucca, A. (In press). A local-global principle for polyquadratic twists of abelian surfaces. Indiana University Mathematics Journal.
Peer Reviewed verified by ORBi

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

PERUCCA, A. (In press). Cardinalities and the continuum hypothesis.

PERUCCA, A. (In press). The decimal representation of a fraction. Uitwiskeling.

Meyrath, T., Mincu, C.-I., & Perucca, A. (In press). Training mathematical thinking with the inclusive card game UNO. In Beiträge zum Mathematikunterricht (Tagungsband GDM) (2024). WTM-Verlag Münster.

Perucca, A. (In press). Advertisement for mathematical competitions.

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). Number theorist mug.

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

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., Seuré, T., & Wolff, V. (2024). Divisibility Graphs: Graphs representing modular multiplications. American Mathematical Monthly.
Peer Reviewed verified by ORBi

PERUCCA, A. (2024). SuperPLUS Poster.

Perissinotto, F., & Perucca, A. (2023). Kummer theory for products of one-dimensional tori. Publications Mathematiques de Besançon, 2023, 109-119.
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). 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. (2023). BIGsmall.

PERUCCA, A. (2023). Horizontal.

PERUCCA, A. (2023). BIG.

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

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.

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

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

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

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. (2022). Silent Danger.

Perucca, A. (2022). Visual Mathematical Dictionary. (Mitteilungen der Gesellschaft für Didaktik der Mathematik).

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). The Hardest Logic Puzzle Ever. Plus Magazine.

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). Staircase numbers. Uitwiskeling.

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

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

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., & Stranen, D. (2020). Converting the Old Babylonian Tablet ‘Plimpton 322’ into the Decimal System as a Classroom Exercise. Convergence.
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

Begalla, E., & Perucca, A. (2020). The ABCD of cyclic quadrilaterals. Uitwiskeling.

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

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

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

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. (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). The PytEuk puzzle.

Perucca, A. (2018). Math around the Clock. 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. doi:10.1142/S1793042117500828
Peer reviewed

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

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

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

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

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

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

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.). Saddle point walk.

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

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

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.

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

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

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.). Mathematical Escape Game Sample Riddle.

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

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

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

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.

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

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

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

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

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

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.). Full availability.

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

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.). Math in Disguise: Constructing Braids.

Peric, M., & Perucca, A. (n.d.). Mathematics of the Vichten Mosaic. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55369.

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

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

PERUCCA, A. (n.d.). Friendly mathematical exercises.

Perucca, A. (n.d.). Congruence theorems for convex polygons involving heights. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/55781.

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.). Didactics without borders.

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