On an equation involving fractional powers with one prime and one almost prime variables

2016/04/13 by Petrov, Zhivko, Tolev, Doychin
#11P05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1604.03885

Abstract

In this paper we consider the equation [p^c] + [m^c] = N, where N is a sufficiently large integer, and prove that if 1 < c < (29)/(28), then it has a solution in a prime p and an almost prime m with at most [ (52)/(29 - 28 c)] + 1 prime factors.

Related

• On an equation involving fractional powers with prime numbers of a\n special type
• On the equation x₁² + x₂² + x₃² + x₄² = N with variables such that x₁ x₂ x₃ x₄ + 1 is an almost-prime
• Waring-Goldbach Problem: One Square, Four Cubes and Higher Powers
• On an additive problem involving fractional powers with one prime and an almost prime variables
• Almost primes of the form [p^1/γ]