Some congruence properties of binomial coefficients and linear second order recurrences

Neville Robbins

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-8

Abstract:

Using elementary methods, the following results are obtained:(I) If p is prime, 0 ≤ m ≤ n , 0 < b < a p n − m , and p ∤ a b , then ( a p n b p m ) ≡ ( − 1 ) p − 1 ( a p b n − m ) ( mod p n ) ; If r , s are the roots of x 2 = A x − B , where ( A , B ) = 1 and D = A 2 − 4 B > 0 , if u n = r n − s n r − s , v n = r n + s n , and k ≥ 0 , then (II) v k p n ≡ v k p n − 1 ( mod p n ) ; (III) If p is odd and p ∤ D , then u k p n ≡ ( D p ) u k p n − 1 ( mod p n ) ; (IV) u k 2 n ≡ ( − 1 ) B u k 2 n − 1 ( mod 2 n ) .

Date: 1988
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/11/134913.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/11/134913.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:134913

DOI: 10.1155/S0161171288000900

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().