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SUMMARY:Daniel Baczkowski (University of Findlay)
DTSTART:20250520T203000Z
DTEND:20250520T205500Z
DTSTAMP:20260423T010423Z
UID:CANT2025/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/25/
 ">Diophantine equations involving arithmetic functions and factorials</a>\
 nby Daniel Baczkowski (University of Findlay) as part of Combinatorial and
  additive number theory (CANT 2025)\n\nLecture held in CUNY Graduate Cente
 r - Science Center (4th floor).\n\nAbstract\nF. Luca proved for any fixed 
 rational number $\\alpha>0$ that the Diophantine equations $\\alpha\\\,m!=
 f(n!)$\, where $f$ is either the Euler function\, the divisor sum function
 \, or the function counting the number of divisors\, have finitely many in
 teger solutions in~$m$ and~$n$. In joint work with Novakovi\\'{c} we gener
 alize the mentioned result and show that Diophantine equations of the form
  $\\alpha\\\,m_1!\\cdots m_r!=f(n!)$ have finitely many integer solutions\
 , too. In addition\, we do so by including the case $f$ is the sum of $k$\
 \textsuperscript{th} powers of divisors function. Moreover\, the same hold
 s by replacing some of the factorials with certain examples of Bhargava fa
 ctorials.\n
LOCATION:https://researchseminars.org/talk/CANT2025/25/
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