Diophantine Approximation with Products of Two Primes

Abstract

We show that for any irrational $\alpha$ and any $\tau <8/23$ there are infinitely many $n$ which are the product of two primes for which $$\Vert n\alpha \Vert \le n^{-\tau }.$$ We also show that for all sufficiently large $b$ there exist 3-digit palindromes in base $b$ with precisely two prime factors.

25 pages

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• Reversible primes