Negation of binomial coefficients
β Scribed by Renzo Sprugnoli
- Book ID
- 108113917
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 139 KB
- Volume
- 308
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let r ) 1 and s ) 0 be arbitrary real numbers. Using Stirling's formula, n n Ε½ n.
We prove that if the signed binomial coefficient (-1) i k i viewed modulo p is a periodic function of i with period h in the range 0 i k, then k + 1 is a power of p, provided h is not too large compared to k. (In particular, 2h k suffices). As an application, we prove that if G and H are multiplicat
The Lucas theorem for binomial coefficients implies some interesting tensor product properties of certain matrices regarded for every prime p in the field TP. Let us define the array of numbers C(i,j) for all nonnegative integers i and j by binomial coefficients: ## 0 _i ' We may display the numb
For p prime and i < p, i # 0, (r;Ti) I (r + l)(r;l) (y) (mod p2). A parallel, but rather different congruence holds modulo p3. In 1878, kdouard Lucas gave an elegant result for computing binomial coefficients modulo a prime [1,2]. H is result is as follows.