http://hdl.handle.net/11320/8761 2026-03-07T18:29:41Z 2026-03-07T18:29:41Z Pąk, Karol http://hdl.handle.net/11320/19740 2026-02-02T13:53:08Z 2025-01-01T00:00:00Z

Tytuł: Elementary Number Theory Problems. Part XIX Autorzy: Pąk, Karol Abstrakt: In this paper, we present formal solutions to twelve problems selected from Wacław Sierpiński’s book 250 Problems in Elementary Number Theory. The selected problems are: 108, 112–114, 118–119, 127, 129, 130, and 132–134 formalized in the Mizar system.

2025-01-01T00:00:00Z Grabowski, Adam http://hdl.handle.net/11320/19737 2026-02-02T12:02:22Z 2025-01-01T00:00:00Z

Tytuł: Elementary Number Theory Problems. Part XVIII Autorzy: Grabowski, Adam Abstrakt: In this paper another seven problems from Wacław Sierpiński’s book “250 Problems in Elementary Number Theory” are formalized, using the Mizar formalism, namely: 53, 61, 81, 90, 100, 156, and 167.

2025-01-01T00:00:00Z Korniłowicz, Artur Naumowicz, Adam http://hdl.handle.net/11320/19732 2026-02-02T08:30:40Z 2025-01-01T00:00:00Z

Tytuł: Elementary Number Theory Problems. Part XVII Autorzy: Korniłowicz, Artur; Naumowicz, Adam Abstrakt: This paper furthers the formalization of problems from Wacław Sierpiński book “250 Problems in Elementary Number Theory” in the Mizar system. The selected twelve items are 37, 101, 115, 117, 145, 157, 159, 161–163, 165, and 169.

2025-01-01T00:00:00Z Pąk, Karol http://hdl.handle.net/11320/19594 2026-01-09T11:44:21Z 2025-01-01T00:00:00Z

Tytuł: Conway’s Normal Form in the Mizar System Autorzy: Pąk, Karol Abstrakt: This paper presents a formal definition of the Conway normal form, a structured representation uniquely suited to characterising surreal numbers by expressing them as sums within a hierarchically ordered group. To this end, we formalise the first sections of the chapter The Structure of the General Surreal Number in Conway’s book. In particular, we define omega maps and prove the existence and uniqueness of the Conway name for surreal numbers.

2025-01-01T00:00:00Z