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SUMMARY:Florian Luca (Stellenbosch University\, South Africa)
DTSTART:20260718T173000Z
DTEND:20260718T175500Z
DTSTAMP:20260710T111524Z
UID:CANT2026/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2026/86/
 ">Multiply gleeful numbers</a>\nby Florian Luca (Stellenbosch University\,
  South Africa) as part of Combinatorial and additive number theory seminar
  (CANT 2026)\n\nLecture held in Science Center in the CUNY Graduate Center
  (4th floor).\n\nAbstract\nFor positive integers $k$ and $n$ let $f_k(n)$ 
 be the number of ways of representing $n$ as a sum of $k$ powers of consec
 utive primes. A number is called $k$-gleeful if \n$f_k(n)>0$ and multiply 
 gleeful if $f_k(n)>1$ or $f_k(n)f_{k'}(n)>0$ for some positive integers $k
 < k'.$ Under Schinzel's hypothesis H\, we show that there are infinitely m
 any positive integers $n$ such that $f_2(n)f_4(n)>0$. Under the same assum
 ption we show that $\\limsup_{n\\to\\infty} f_2(n)=\\infty$. This gives a 
 conditional proof of a stronger version of a conjecture of Moore and Soren
 son from the preprint arXiv:2507.09012v1\, July 2025.\n
LOCATION:https://researchseminars.org/talk/CANT2026/86/
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