In a recent article, Apagodu and Zeilberger discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequences. At the end, they propose some supercongruences as conjectures. Here we prove one of them, including a new companion enumerating Abelian squares, and we leave some remarks for the others
Following an idea of Rowland [Row] we give a conjectural way to gen-erate increasing sequences of pr...
The most famous open problems concerning prime numbers are binary additive problems, with the twin-p...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In a recent article, Apagodu and Zeilberger discuss some applications of an algorithm for finding an...
Text. We prove congruences, modulo a power of a prime p, for certain finite sums involving central b...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamond p...
A generalized central trinomial coefficient Tn(b, c) is the coefficient of xn in the expansion of (x...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding [Form...
International audienceGiven a multiplicative function~$f$ which is periodic over the primes, we obta...
In this thesis we use recent versions of the Circle Method to prove three theorems in the area of ad...
Jacobi’s two-square theorem states that the number of representations of a positive integer k as a s...
Following an idea of Rowland [Row] we give a conjectural way to gen-erate increasing sequences of pr...
The most famous open problems concerning prime numbers are binary additive problems, with the twin-p...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
In a recent article, Apagodu and Zeilberger discuss some applications of an algorithm for finding an...
Text. We prove congruences, modulo a power of a prime p, for certain finite sums involving central b...
AbstractWe present several congruences for sums of the type ∑k=1p−1mkk−r(2kk)−1, modulo a power of a...
Recently the first author proved a congruence proposed in 2006 by Adamchuk: Sigma([2p/3])(k=1) (2k k...
Abstract. Much is known about binomial coefficients where primes are con-cerned, but considerably le...
In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamond p...
A generalized central trinomial coefficient Tn(b, c) is the coefficient of xn in the expansion of (x...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding [Form...
International audienceGiven a multiplicative function~$f$ which is periodic over the primes, we obta...
In this thesis we use recent versions of the Circle Method to prove three theorems in the area of ad...
Jacobi’s two-square theorem states that the number of representations of a positive integer k as a s...
Following an idea of Rowland [Row] we give a conjectural way to gen-erate increasing sequences of pr...
The most famous open problems concerning prime numbers are binary additive problems, with the twin-p...
AbstractIt is conjectured that all sufficiently large integers satisfying some necessary congruence ...
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