Publication Date:
2014-03-28
Description:
Let $\|x\|$ denote the distance from $x$ to the nearest integer. We show that for any irrational $\alpha$ and for any $\tau 〈 \frac {8}{23},$ there are infinitely many $n$ which are the product of two primes for which \[\|n\alpha \|\leq n^{-\tau }.\] We also show that for all sufficiently large $b$ there exist $3$ -digit palindromes in base $b$ with precisely two prime factors.
Print ISSN:
0024-6107
Electronic ISSN:
1469-7750
Topics:
Mathematics