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arXiv · 1302.6061

Diophantine Approximation with Products of Two Primes

A. J. Irving
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Abstract

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

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A. J. Irving. 2013-02-25. Diophantine Approximation with Products of Two Primes. https://doi.org/10.1112/jlms%2Fjdt079

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