Polynomial congruences over incomplete residue systems, modulo k
نویسندگان
چکیده
منابع مشابه
Gray Images of Constacyclic Codes over some Polynomial Residue Rings
Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( . The Gray map is said to be a ( )-Gray map if the image of any -constacyclic code over is a -constacyclic code over the field . In this paper we investigate the existence of ( )-Gray maps over . In this direction, we find an equivalent ...
متن کاملCongruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If α > 1 and l, s, t are nonnegative integers with s, t < p, then 1 ⌊n/p α−1 ⌋! k≡r (...
متن کاملCombinatorial Congruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f(x) ∈ Z[x]. We establish the congruence p f ∑ k≡r (mod pα) (n k ) (−1)f ( k − r pα ) ≡ 0 ( mod p ∑∞ i=α n/p i ) (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas’ theorem: If α is greater than one, and l, s, t are nonnegative integers with s, t < p, then 1 ...
متن کاملSome Curious Congruences modulo Primes
Let n be a positive odd integer and let p > n + 1 be a prime. We mainly derive the following congruence: ∑ 0<i1<···<in<p ( i1 3 ) (−1)i1 i1 · · · in ≡ 0 (mod p).
متن کاملDerived from Polynomial Congruences modulo m and Generalized Fermat’s Little Theorem
This paper mainly studies problems about so called “bijective polynomials modulo m”. This research is from The most important result derived from this research is the following generalized Fermat’s Little Theorem (note that this is just a simpler version of Theorem 17 in Sec. 5). Theorem 17 Assume p1, · · · , pr are r different prime numbers, d1, · · · , dr ≥ 1, m = p d1 1 · · · p dr r , D = ∑r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1989
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(89)80016-2