It is proved that the number of a ∈ {1, · · · , p − 1} which can be represented as a product of two factorials is at least 3 4 p+O(p1/2(log p)2). This improves the result given by Garaev et.al. [Trans. Amer. Math. Soc., 356 (2004)5089-5102]. Beyond this, we pose several conjectures
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
Abstract. Let p be a prime number, J a set of consecutive integers, Fp the algebraic closure of Fp =...
Let bℓ(n) denote the number of ℓ -regular cubic partition pairs of n. In this paper, we establi...
It is proved that the number of a ∈ {1, · · · , p − 1} which can be represented as a product of t...
We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ ...
Let p be a fixed odd prime and let s and t be fixed positive integers which depend on p. Consider th...
As a consequence of Wilson’s theorem, the factorial ((p−1)/2) ! mod p provides a square root of (−...
AbstractWe present several elementary theorems, observations and questions related to the theme of c...
Abstract. We present several elementary theorems, observations and ques-tions related to the theme o...
We determine the positive integers n such that all of the coefficients in the expansion of the multi...
Write a equivalent to 3 . 2(-1) and b equivalent to 3 . 2(-2) (mod p) where p is an odd prime. Let c...
Recently, several bounds have been obtained on the number of solutions of congruences of the type (x...
In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamond p...
The arithmetic properties of the ordinary partition function p(n) have been the topic of intensive s...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
Abstract. Let p be a prime number, J a set of consecutive integers, Fp the algebraic closure of Fp =...
Let bℓ(n) denote the number of ℓ -regular cubic partition pairs of n. In this paper, we establi...
It is proved that the number of a ∈ {1, · · · , p − 1} which can be represented as a product of t...
We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xv + s) ≡ ...
Let p be a fixed odd prime and let s and t be fixed positive integers which depend on p. Consider th...
As a consequence of Wilson’s theorem, the factorial ((p−1)/2) ! mod p provides a square root of (−...
AbstractWe present several elementary theorems, observations and questions related to the theme of c...
Abstract. We present several elementary theorems, observations and ques-tions related to the theme o...
We determine the positive integers n such that all of the coefficients in the expansion of the multi...
Write a equivalent to 3 . 2(-1) and b equivalent to 3 . 2(-2) (mod p) where p is an odd prime. Let c...
Recently, several bounds have been obtained on the number of solutions of congruences of the type (x...
In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamond p...
The arithmetic properties of the ordinary partition function p(n) have been the topic of intensive s...
AbstractLet θ(k, p) be the least s such that the congruence x1k + … + xsk ≡ 0(mod p) has a nontrivia...
AbstractLetRbe a UFD andpa prime ofR. Letl1a1,…,lrarbe prime top. In this paper a formula is derived...
Abstract. Let p be a prime number, J a set of consecutive integers, Fp the algebraic closure of Fp =...
Let bℓ(n) denote the number of ℓ -regular cubic partition pairs of n. In this paper, we establi...
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