We show that there is no square other than 122 and 7202 such that it can be written as a product of k−1 integers out of k(≥3) consecutive positive integers. We give an extension of a theorem of Sylvester that a product of k consecutive integers each greater than k is divisible by a prime exceeding k
In this paper based on a sort of linear function, a deterministic and simple algorithm with an algeb...
A classical theorem discovered independently by J. Sylvester [8], and I. Schur [7], states that the ...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
A classical result of Sylvester [21] (see also [16], [17]), generalizing Bertrand’s Postulate, state...
This paper mainly concerns itself with squares expressible as sum of consecutive squares. Let | be t...
It is proved that a product of four or more terms of positive integers in arithmetic progression wit...
An old conjecture of Erdos and Graham states that only finitely many integer squares could be obtain...
It is shown under Schinzel's Hypothesis that for a given l≥ 1, there are infinitely many k such that...
In this article, we study short intervals that contain “almost squares” of the type: any integer n w...
AbstractIn this paper, we construct, given an integer r≥5, an infinite family of r non-overlapping b...
We prove that the product of first n consecutive values of the polynomial P(k) = 4k(4) + 1 is a perf...
Abstract. It is shown under Schinzel’s Hypothesis that for a given ` ≥ 1, there are infinitely many...
We show that for any positive integer n, there is some fixed A such that d(x)=d(x+n)=A infinitely of...
AbstractLet k ≥ 4 be an integer. We find all integers of the form byl where l ≥ 2 and the greatest p...
We find an infinite family of positive integers a such that concatenating a and a − 1 in base 10 (fr...
In this paper based on a sort of linear function, a deterministic and simple algorithm with an algeb...
A classical theorem discovered independently by J. Sylvester [8], and I. Schur [7], states that the ...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
A classical result of Sylvester [21] (see also [16], [17]), generalizing Bertrand’s Postulate, state...
This paper mainly concerns itself with squares expressible as sum of consecutive squares. Let | be t...
It is proved that a product of four or more terms of positive integers in arithmetic progression wit...
An old conjecture of Erdos and Graham states that only finitely many integer squares could be obtain...
It is shown under Schinzel's Hypothesis that for a given l≥ 1, there are infinitely many k such that...
In this article, we study short intervals that contain “almost squares” of the type: any integer n w...
AbstractIn this paper, we construct, given an integer r≥5, an infinite family of r non-overlapping b...
We prove that the product of first n consecutive values of the polynomial P(k) = 4k(4) + 1 is a perf...
Abstract. It is shown under Schinzel’s Hypothesis that for a given ` ≥ 1, there are infinitely many...
We show that for any positive integer n, there is some fixed A such that d(x)=d(x+n)=A infinitely of...
AbstractLet k ≥ 4 be an integer. We find all integers of the form byl where l ≥ 2 and the greatest p...
We find an infinite family of positive integers a such that concatenating a and a − 1 in base 10 (fr...
In this paper based on a sort of linear function, a deterministic and simple algorithm with an algeb...
A classical theorem discovered independently by J. Sylvester [8], and I. Schur [7], states that the ...
The Fundamental Theorem of Arithmetic is usually stated in a form emphasizing how primes enter the s...
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