On Sums of Primes from Beatty Sequences
نویسنده
چکیده
Ever since the days of Euler and Goldbach, number-theorists have been fascinated by additive representations of the integers as sums of primes. The most famous result in this field is I.M. Vinogradov’s three primes theorem [7], which states that every sufficiently large odd integer is the sum of three primes. Over the years, a number of authors have studied variants of the three primes theorem with prime numbers restricted to various sequences of arithmetic interest. For instance, a recent work by Banks, Güloğlu and Nevans [1] studies the question of representing integers as sums of primes from a Beatty sequence. Suppose that α and β are real numbers, with α > 1 and irrational. The Beatty sequence Bα,β is defined by
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