CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS III

Author:

SUN ZHI-HONG1

Affiliation:

1. School of Mathematical Sciences, Huaiyin Normal University, Huaian, Jiangsu 223001, P. R. China

Abstract

Suppose that p is an odd prime and d is a positive integer. Let x and y be integers given by p = x2+dy2 or 4p = x2+dy2. In this paper we determine x( mod p) for many values of d. For example, [Formula: see text] where x is chosen so that x ≡ 1 ( mod 3). We also pose some conjectures on supercongruences modulo p2 concerning binary quadratic forms.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Cited by 6 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Congruences concerning truncated hypergeometric series;Proceedings of the Royal Society of Edinburgh: Section A Mathematics;2017-03-16

2. Supercongruences on Truncated Hypergeometric Series;Results in Mathematics;2016-12-21

3. Supercongruences and truncated hypergeometric series;Proceedings of the American Mathematical Society;2016-08-18

4. CERTAIN COMBINATORIC CONVOLUTION SUMS AND THEIR RELATIONS TO BERNOULLI AND EULER POLYNOMIALS;Journal of the Korean Mathematical Society;2015-05-01

5. Proof of a supercongruence conjectured by Z.-H. Sun;Integral Transforms and Special Functions;2014-10-08

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