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Bracket Function Congruences for Binomial Coefficients

✍ Scribed by L. Carlitz and H. W. Gould

Book ID
120251192
Publisher
Mathematical Association of America
Year
1964
Tongue
English
Weight
293 KB
Volume
37
Category
Article
ISSN
0025-570X

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πŸ“œ SIMILAR VOLUMES

Congruences for sums of binomial coeffic
Congruences for sums of binomial coefficients
✍ Zhi-Wei Sun; Roberto Tauraso πŸ“‚ Article πŸ“… 2007 πŸ› Elsevier Science 🌐 English βš– 135 KB

Let q > 1 and m > 0 be relatively prime integers. We find an explicit period Ξ½ m (q) such that for any integers n > 0 and r we have whenever a is an integer with gcd(1 -(-a) m , q) = 1, or a ≑ -1 (mod q), or a ≑ 1 (mod q) and 2 | m, where n r m (a) = k≑r (mod m) n k a k . This is a further extensio

Some binomial coefficient congruences
Some binomial coefficient congruences
✍ D.F. Bailey πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 297 KB

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.