Numbers representable by five prime squares with primes in an arithmetic progression
O osmém Hilbertově problému
On a conjecture of Yiming Long
On a diophantine inequality involving prime numbers
On a diophantine problem with one prime, two squares of primes and s powers of two
On a Diophantine problem with two primes and s powers of two
On a problem of Hardy and Littlewood
On a problem of the Additive Theory of Numbers
On a system of two diophantine inequalities with prime numbers
On a system of two diophantine inequalities with prime numbers
On an additive problem of unlike powers in short intervals
We prove that almost all positive even integers can be represented as with for . As a consequence, we show that each sufficiently large odd integer can be written as with for .
On an equation with prime numbers
On Binary Equations.
On Generalized Quadratic Equations in Three Prime Variables.
On Goldbach's problem
On integers of the form
On Linnik's approximation to Goldbach's problem, I
On Linnik's theorem on Goldbach numbers in short intervals and related problems
Linnik proved, assuming the Riemann Hypothesis, that for any , the interval contains a number which is the sum of two primes, provided that is sufficiently large. This has subsequently been improved to the same assertion being valid for the smaller gap , the added new ingredient being Selberg’s estimate for the mean-square of primes in short intervals. Here we give another proof of this sharper result which avoids the use of Selberg’s estimate and is therefore more in the spirit of Linnik’s...
On pairs of Goldbach-Linnik equations with unequal powers of primes
It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.
On pairs of linear equations in three prime variables and an application to Goldbach's problem.