Congruences concerning Legendre polynomials II
Copyright policy )Congruences concerning Legendre polynomials II
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.
- Huainan Normal University China (People's Republic of)
- Huaiyin Normal University China (People's Republic of)
- School of Mathematical Sciences
- Huaiyin Normal University China (People's Republic of)
- Huainan Normal University China (People's Republic of)
Mathematics - Number Theory, 11A07, 33C45, 11E25, 11L10, 05A10, 05A19, 11B39, congruence, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Legendre polynomial, FOS: Mathematics, Mathematics - Combinatorics, Congruences; primitive roots; residue systems, Number Theory (math.NT), Combinatorics (math.CO), Sums of squares and representations by other particular quadratic forms, binary quadratic form, 11A07, 33C45, 11E25, 11L10, 05A10, Factorials, binomial coefficients, combinatorial functions
Mathematics - Number Theory, 11A07, 33C45, 11E25, 11L10, 05A10, 05A19, 11B39, congruence, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Legendre polynomial, FOS: Mathematics, Mathematics - Combinatorics, Congruences; primitive roots; residue systems, Number Theory (math.NT), Combinatorics (math.CO), Sums of squares and representations by other particular quadratic forms, binary quadratic form, 11A07, 33C45, 11E25, 11L10, 05A10, Factorials, binomial coefficients, combinatorial functions
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