On the distribution of some integers related to perfect and amicable numbers
On the exceptional set of Lagrange’s equation with three prime and one almost–prime variables
We consider an approximation to the popular conjecture about representations of integers as sums of four squares of prime numbers.
On the independence of σ(ϕ(n)) and ϕ(σ(n))
On the Integers Relatively Prime to n and a Number-Theoretic Function Considered by Jacobsthal.
On the intervals between numbers that are sums of two squares: IV.
On the irrationality of a divisor function series.
On the largest prime factor of integers
On the least almost-prime in arithmetic progression
Let denote an almost-prime with at most prime factors, counted according to multiplicity. Suppose that and are positive integers satisfying . Denote by the least almost-prime which satisfies . It is proved that for sufficiently large , there holds This result constitutes an improvement upon that of Iwaniec (1982), who obtained the same conclusion, but for the range in place of .
On the least almost-prime in arithmetic progressions
Let denote a positive integer with at most prime factors, counted according to multiplicity. For integers , such that , let denote the least in the arithmetic progression . It is proved that for sufficiently large , we have This result constitutes an improvement upon that of J. Li, M. Zhang and Y. Cai (2023), who obtained
On the moments of the Carmichael λ function
On the number of prime divisors of the order of elliptic curves modulo p
On the number of prime factors of integers of the form ab + 1
On the number of solutions of N - p = Pr.
On the number-theoretic functions ν(n) and Ω(n)
On the order of vanishing of modular -functions at the critical point
On the periods of the linear congruential and power generators
On the Piatetski-Shapiro-Vinogradov Theorem
On the problem of Goldbach's type.
On the representation of almost primes by pairs of quadratic forms
On the sequence .