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Problem of the Month – December 2022

A positive integer is said to be square free if it is not divisible by a square greater than 1.
We say that a positive integer is simple if each of the numbers a, a + 1 and a + 2 is square
free. Are there infinitely many simple integers?



Correct Solutions by,

  • Toshihiro Shimizu Kawasaki, Japan
  • Choi Min KyuSouth Korea
  • Henrik Aberg Gothenburg, Sweden
  • Roger Bengtsson Lund, Sweden
  • Özgür Soysal Bilkent University
  • Mustafa Burak Topal Istanbul
  • Hüseyin Ege Olcay Bilkent University
  • Güneş Parlakgül Harvard University, USA


Solution: http://www.fen.bilkent.edu.tr/~cvmath/Problem/2212a.pdf