mathematical problem

mathematical problem (tsz. mathematical problems)

1. (informatika) A mathematical problem (matematikai probléma) olyan logikusan megfogalmazott kérdés vagy feladat, amelynek célja egy állítás bizonyítása vagy cáfolása, illetve egy keresett érték meghatározása adott feltételek mellett. Ezek lehetnek elméleti vagy alkalmazott jellegűek, és a matematika minden ágában megtalálhatók: aritmetikától kezdve a topológián át a számelméletig.

Probléma	Leírás
Fermat utolsó tétele	${\textstyle x^{n}+y^{n}=z^{n}}$ nem oldható meg pozitív egészekkel ${\textstyle n>2}$
Goldbach-sejtés	Minden páros szám 2 > 2 előáll két prímszám összegeként
Riemann-sejtés	A zéta-függvény nem triviális gyökei mind valós részükben ${\textstyle {\frac {1}{2}}}$-ek
Gráfszínezés	Minimális színek száma, mellyel egy gráf csúcsai kiszínezhetők úgy, hogy szomszédok ne legyenek egyformák
Deriválás	Függvény változásának meghatározása
Legkisebb közös többszörös	Két szám legkisebb közös oszthatója

1. Bemenet (feltételek) – Adott adatok, kezdeti információk
2. Kimenet (kérdés) – Amit keresünk (bizonyítandó, kiszámítandó, konstruálandó)
3. Megoldás – Olyan lépéssorozat, amely logikai úton a kimenethez vezet

Mely természetes számokra igaz, hogy ${\textstyle x^{2}=49}$?

• ${\textstyle x^{2}=49}$
• ${\textstyle x=\pm 7}$
• Ha csak természetes számokban gondolkodunk, akkor ${\textstyle x=7}$

✅ Megoldás: ${\textstyle x=7}$

Szint	Példa
Könnyű	Elsőfokú egyenlet: ${\textstyle 2x+1=5}$
Közepes	Kombinatorikai elrendezések
Nehéz	Integrálás, differenciálegyenlet
Extrém	Millennium-problémák, NP-teljes bizonyítás

1. Riemann-sejtés
2. Navier–Stokes-egyenletek
3. P vs NP
4. Hodge-sejtés
5. Yang–Mills elmélet
6. Birch–Swinnerton-Dyer sejtés
7. Poincaré-sejtés ✅ (Perelman megoldotta)

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