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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)
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 (123)
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others (5)
Arts & humanities: Multidisciplinary, general & others (4)
Languages & linguistics (2)
Engineering, computing & technology: Multidisciplinary, general & others (1)

Publications (total 137)

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

The most cited

19 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. (In press). Friendly mathematical exercises.

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

PERUCCA, A. (In press). Math CEO (of AI).

Fité, F., & PERUCCA, A. (In press). 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). 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. (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., & 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.

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). Cardinalities and the continuum hypothesis. Uitwiskeling.

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

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

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. (2024). Didactics without borders.

PERUCCA, A. (2024). A note on Kneser's theory. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/62415.

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

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). 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). BIGsmall.

PERUCCA, A. (2023). BIG.

PERUCCA, A. (2023). Horizontal.

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.

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

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). Visual Mathematical Dictionary.

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). Minorities in Mathematics. MaddMaths!.

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., & 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

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.

PERUCCA, A. (2021). Staircase numbers. 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

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., & 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. (2020). Kummer theory for number fields and the reductions of algebraic numbers II. Uniform Distribution Theory. doi:10.1142/S179304211950091X
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.

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 seven bridges of Königsberg. Uitwiskeling.

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

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

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 problem of detecting linear dependence. Rivista di Matematica della Universita di Parma.
Peer reviewed

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

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 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.). Quadratic equations: from trivial to impossible.

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

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.). MatheMAGICAL: Guess the number.

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

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

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

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.). Unconscious assumptions in mathematical examples. ORBilu-University of Luxembourg. https://orbilu.uni.lu/handle/10993/50582.

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

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

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

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

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.). 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.). Role models for minorities in mathematics.

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

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

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.). 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.). 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.). 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.

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., 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.). Math in disguise.

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.

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

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

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.

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

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

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

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

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.

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

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

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.). A didactical reflection on varying quantities.

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