Add to ORKGIn this paper we study vp(n!), the greatest power of prime p in factorization of n!. We find some lower and upper bounds for vp(n!), and we show that vp(n!) = (n/p−1) + O(ln n). By using above mentioned bounds, we study the equation vp(n!) = v for a fixed positive integer v. Also, we study the triangle inequality about vp(n!), and show that the inequality pvp(n!) > qvq(n!) holds for primes p < q and sufficiently large values of n
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...
AbstractIf n is a positive integer, we write n! as a product of n prime powers, each at least as lar...
AbstractLet p, q be primes and m be a positive integer. For a positive integer n, let ep(n) be the n...
summary:Let $p_{1}, p_{2}, \cdots $ be the sequence of all primes in ascending order. Using explicit...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractThe parity of exponents in the prime power factorization of n! is considered. We extend and ...
In this note, we show that the ABC-conjecture implies that a diophantine equation of the form P(x) =...
Erd\"os and Obl\'ath proved that the equation $n!\pm m!=x^p$ has only finitely many integer solution...
We prove under a mild condition that Kurepa's conjecture holds for the set of prime numbers \(p\) su...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
Let d(m) be the number of divisors of the positive integer m. Here, we show that if n {3,5}, then d(...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...
AbstractIf n is a positive integer, we write n! as a product of n prime powers, each at least as lar...
AbstractLet p, q be primes and m be a positive integer. For a positive integer n, let ep(n) be the n...
summary:Let $p_{1}, p_{2}, \cdots $ be the sequence of all primes in ascending order. Using explicit...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractThe parity of exponents in the prime power factorization of n! is considered. We extend and ...
In this note, we show that the ABC-conjecture implies that a diophantine equation of the form P(x) =...
Erd\"os and Obl\'ath proved that the equation $n!\pm m!=x^p$ has only finitely many integer solution...
We prove under a mild condition that Kurepa's conjecture holds for the set of prime numbers \(p\) su...
AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, giv...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
Let d(m) be the number of divisors of the positive integer m. Here, we show that if n {3,5}, then d(...
In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only fi...
AbstractTwo results are obtained about P(n), the largest prime factor of an integer n. The average v...
For a set of primes P, let Ψ(x;P) be the number of positive integers n≤x all of whose prime factors ...