关于勒让德多项式模p^2的同余

Q3 Mathematics

Communications in Mathematics Pub Date : 2023-02-14 DOI:10.46298/cm.10767

Aeran Kim

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引用次数: 0

摘要

In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P P - 1 2 (x) to P P +1 2 (x) for odd prime P;which enables us to deduce some congruences resembling p + 1 2∑k = 0 4pk 16 k (2k + 4k 2 - 1, - 1) 2 (2k k) 2 (mod p 2)。这篇论文中,我们z·h·sun的章吱扭다항식的联合式p 2 (x)在p - 1, p = p + 1 2 (x)段,p是质数)到利用类似联合式的联合式p + 1 2∑k = 0 4pk 16 k (2k + 4k 2 - 1, - 1) 2 (2k k) 2 (mod p 2)诱导的。

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CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS MODULO p^2

In this article, we extend Z. H. Sun's congruences concerning Legendre polynomials P p−1 2 (x) to P p+1 2 (x) for odd prime p, which enables us to deduce some congruences resembling p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2). 이 논문에서 우리는 Z. H. Sun의 르장드르 다항식의 합동식 P p−1 2 (x) 에서 P p+1 2 (x) (단, p는 소수) 까지를 이용해서 이 합동식과 비슷한 합동식 p+1 2 ∑ k=0 4pk + 4k 2 − 1 16 k (2k − 1) 2 (2k k)2 (mod p 2) 을 유도한다.

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来源期刊

Communications in Mathematics Mathematics-Mathematics (all)

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

45 weeks

期刊介绍： Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.