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Puzzling

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  • $\begingroup$ Does "as far as I know" mean that you merely suspect (but do not know for certain) that there are infinitely many integers with the property? $\endgroup$
    – msh210
    Commented Aug 21, 2023 at 18:45
  • $\begingroup$ I practically know, but I don't know how to prove it. $\endgroup$
    – Peter
    Commented Aug 21, 2023 at 19:13
  • $\begingroup$ just to be sure: 84, 96 and 108 are the first(and smallest) numbers in the sequence, right? $\endgroup$
    – Novarg
    Commented Aug 22, 2023 at 8:15
  • 1
    $\begingroup$ @Novarg Yes, that's correct. $\endgroup$
    – Peter
    Commented Aug 22, 2023 at 10:37
  • 2
    $\begingroup$ @DmitryKamenetsky Sure! I might have made this puzzle a little too difficult - not because it's clever but because it's not good; it sort of requires an intuitive leap, which should be avoided. But I didn't want to delete it either, since at least a couple of people have worked very well to come closer to a solution. $\endgroup$
    – Peter
    Commented Aug 25, 2023 at 13:53