Aminomethylation of Thioureas with N,N-Dimethyl-1-(triethylsiloxy)methanamine, Involving Amino Group Exchange
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Award ID(s):
Publication Date:
NSF-PAR ID:
10148962
Journal Name:
Russian Journal of Organic Chemistry
Volume:
55
Issue:
11
Page Range or eLocation-ID:
1764 to 1771
ISSN:
1070-4280
1. Abstract We show that for some even $k\leqslant 3570$ and all  $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi$ is Euler’s totient function. We also show that for a positive proportion of all $k$, the equation $\sigma (n)=\sigma (n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath.