Autor: Sun, Zhi - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Artykuł

Skocz do pozycji: 2.

Artykuł

Skocz do pozycji: 3.

Artykuł

Skocz do pozycji: 4.

Artykuł

Skocz do pozycji: 5.

Tytuł:: Fibonacci numbers and Fermats last theorem
Autorzy:: Sun, Zhi-Wei
Powiązania:: https://bibliotekanauki.pl/articles/1391981.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Opis:: Let {Fₙ} be the Fibonacci sequence defined by F₀=0, F₁=1, $F_{n+1}=Fₙ+F_{n-1} (n≥1)$. It is well known that $F_{p-(5//p)}≡ 0 (mod p)$ for any odd prime p, where (-) denotes the Legendre symbol. In 1960 D. D. Wall [13] asked whether $p²|F_{p-(5//p)}$ is always impossible; up to now this is still open.
In this paper the sum $∑_{k≡ r (mod 10)}{n\choose k}$ is expressed in terms of Fibonacci numbers. As applications we obtain a new formula for the Fibonacci quotient $F_{p-(5/p)}/p$ and a criterion for the relation $p|F_{(p-1)//4}$ (if p ≡ 1 (mod 4), where p ≠ 5 is an odd prime. We also prove that the affirmative answer to Wall's question implies the first case of FLT (Fermat's last theorem); from this it follows that the first case of FLT holds for those exponents which are (odd) Fibonacci primes or Lucas primes.
Źródło:: Acta Arithmetica; 1991-1992, 60, 4; 371-388
0065-1036
Pojawia się w:: Acta Arithmetica
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 6.

Artykuł

Skocz do pozycji: 7.

Tytuł:: Study on characteristics of three-dimensional granular meso-reconstruction of coal gangue roadbed
Autorzy:: Fan, Xiang-Xi
Hui, Bing
Ma, Shi-Jie
Fu, Jian-Cun
Zhang, Wen-Jun
Meng, Ling-Xiao
Sun, Zhi
Powiązania:: https://bibliotekanauki.pl/articles/2086979.pdf
Data publikacji:: 2022
Wydawca:: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:: coal gangue roadbed
particle flow
mesoscopic reconstruction
particle breakage
Opis:: The dynamic evolution process of the coal gangue particles’ core retention phenomenon in the process of crushing under stress, the evolution law of grading and the corresponding microscopic mechanical characteristics after continuous particle crushing are analyzed. The meso-level which reveals deformation phenomena of granular materials under the action of external loads is highly complex. At the qualitative level, the static compaction process of coal gangue samples can be roughly divided into three stages: initial compaction stage, compaction and crushing stage, and crushing (compaction) stage. It is proved that the interaction of lateral confined unidirectional compression of granular materials is mainly compression.
Źródło:: Journal of Theoretical and Applied Mechanics; 2022, 60, 3; 361--374
1429-2955
Pojawia się w:: Journal of Theoretical and Applied Mechanics
Dostawca treści:: Biblioteka Nauki

Artykuł

Informacja