Question Number 100622 by MJS last updated on 27/Jun/20

Commented byMJS last updated on 27/Jun/20

building on my work, can someone try to  find the possible values for x∈Q and  x[x[x[x]]]=n∈N ?  in the picture, i and f are the integer and  the fractional part of x

Commented byprakash jain last updated on 03/Jul/20

Q96329 has a special case.  x⌊x⌊x⌊x⌋⌋⌋=n  Trying for general case  x≤⌊n^(1/4) ⌋  x=i+f where i≤⌊n^(1/4) ⌋  x≤n^(1/4) ⇒x⌊x⌊x⌋⌋⌋≥n^(3/4)   induction may help.