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Congruences concerning Legendre polynomials
 PROC. AMER. MATH. SOC
, 2011
"... Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for k=0 k confirm several conjectures of Z.W. Sun. We also pose 13 conjectures on supercongruences. ..."
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Cited by 43 (36 self)
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Let p be an odd prime. In the paper, by using the properties of Legendre polynomials we prove some congruences for k=0 k confirm several conjectures of Z.W. Sun. We also pose 13 conjectures on supercongruences.
PRODUCTS AND SUMS DIVISIBLE BY CENTRAL BINOMIAL COEFFICIENTS
, 2010
"... In this paper we initiate the study of products and sums divisible by central binomial coefficients. We show that ..."
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Cited by 9 (3 self)
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In this paper we initiate the study of products and sums divisible by central binomial coefficients. We show that
WOLSTENHOLME’S THEOREM: ITS GENERALIZATIONS AND EXTENSIONS IN THE LAST HUNDRED AND FIFTY YEARS (1862–2012)
, 2011
"... ..."
Congruences involving ...
, 2013
"... Let p> 3 be a prime, and let m be an integer with p ∤ m. In this paper, based on the work of Brillhart and Morton, by using the work of Ishii and Deuring’s theorem for elliptic curves with complex multiplication we solve some conjectures of ZhiWei Sun concerning p−1 k=0 ..."
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Cited by 1 (1 self)
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Let p> 3 be a prime, and let m be an integer with p ∤ m. In this paper, based on the work of Brillhart and Morton, by using the work of Ishii and Deuring’s theorem for elliptic curves with complex multiplication we solve some conjectures of ZhiWei Sun concerning p−1 k=0
ON DIVISIBILITY CONCERNING BINOMIAL COEFFICIENTS
, 2010
"... Let k,l and n be positive integers. We mainly show that (ln+1) ∣ ( kn+ln k, kn kn ..."
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Let k,l and n be positive integers. We mainly show that (ln+1) ∣ ( kn+ln k, kn kn
3 /m k
"... Abstract. Let p> 3 be a prime, and let m be an integer with p ∤ m. In the paper we p−1 k=0 ..."
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Abstract. Let p> 3 be a prime, and let m be an integer with p ∤ m. In the paper we p−1 k=0
3 p
"... Let p> 3 be a prime, and let Rp be the set of rational numbers whose denominator is not divisible by p. Let {Pn(x)} be the Legendre polynomials. In this paper we mainly show that for m, n, t ∈ Rp with m ≡ 0 (mod p), ..."
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Let p> 3 be a prime, and let Rp be the set of rational numbers whose denominator is not divisible by p. Let {Pn(x)} be the Legendre polynomials. In this paper we mainly show that for m, n, t ∈ Rp with m ≡ 0 (mod p),
K,
, 1102
"... Abstract. Here I give a full list of my conjectures on series for powers of π and other important constants scattered in some of my public preprints. The list contains totally 92 open conjectural series, 87 of which are for 1/π. 1. Various series for some constants ..."
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Abstract. Here I give a full list of my conjectures on series for powers of π and other important constants scattered in some of my public preprints. The list contains totally 92 open conjectural series, 87 of which are for 1/π. 1. Various series for some constants