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BINOMIAL COEFFICIENTS, CATALAN NUMBERS AND LUCAS QUOTIENTS
 SCI. CHINA MATH. 53(2010), IN PRESS.
, 2010
"... Let p be an odd prime and let a,m ∈ Z with a> 0 and p ∤ m. In this paper we determine ∑p a −1 ( 2k k=0 /mk mod p2 for d = 0,1; for k+d example, p a −1 k=0 ..."
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Cited by 43 (36 self)
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Let p be an odd prime and let a,m ∈ Z with a> 0 and p ∤ m. In this paper we determine ∑p a −1 ( 2k k=0 /mk mod p2 for d = 0,1; for k+d example, p a −1 k=0
OPEN CONJECTURES ON CONGRUENCES
, 2010
"... We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 50 unsolved conjectures of the author while conjectures in Part B have been recently confirmed. We hope that this ..."
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Cited by 17 (12 self)
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We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 50 unsolved conjectures of the author while conjectures in Part B have been recently confirmed. We hope that this material will interest number theorists and stimulate further research. Number theorists are welcome to work on those open conjectures.
CONGRUENCES INVOLVING BINOMIAL COEFFICIENTS AND LUCAS SEQUENCES
, 2009
"... In this paper we obtain some congruences involving central binomial coefficients and Lucas sequences. For example, we show that if p> 5 is a prime then p−1 ..."
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Cited by 3 (3 self)
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In this paper we obtain some congruences involving central binomial coefficients and Lucas sequences. For example, we show that if p> 5 is a prime then p−1
CURIOUS CONGRUENCES FOR FIBONACCI NUMBERS
, 2009
"... In this paper we establish some sophisticated congruences involving central binomial coefficients and Fibonacci numbers. For example, we show that if p ̸ = 2, 5 is a prime then and p−1 X k=0 p−1 X k=0 ..."
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Cited by 2 (1 self)
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In this paper we establish some sophisticated congruences involving central binomial coefficients and Fibonacci numbers. For example, we show that if p ̸ = 2, 5 is a prime then and p−1 X k=0 p−1 X k=0
SOME qCONGRUENCES RELATED TO 3ADIC VALUATIONS
, 2009
"... In 1992 Strauss, Shallit and Zagier proved that for any positive integer a we have and furthermore 3 a X−1 k=0 1 ..."
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Cited by 2 (0 self)
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In 1992 Strauss, Shallit and Zagier proved that for any positive integer a we have and furthermore 3 a X−1 k=0 1
Int. J. Number Theory 10(2014), no.3, 793815. CONGRUENCES CONCERNING LUCAS SEQUENCES
, 2013
"... Let p be a prime greater than 3. In this paper, by using expansions and congruences for Lucas sequences and the theory of cubic residues and cubic congruences, we establish some congruences for ∑[p/4] k=0 ..."
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Let p be a prime greater than 3. In this paper, by using expansions and congruences for Lucas sequences and the theory of cubic residues and cubic congruences, we establish some congruences for ∑[p/4] k=0