IMO Shortlist 1994 problem N5
Dodao/la: arhiva2. travnja 2012.
For any positive integer
be the number of elements in the set
whose base 2 representation contains exactly three 1s.
(a) Prove that for any positive integer
, there exists at least one positive integer
(b) Determine all positive integers
for which there exists exactly one
Izvor: Međunarodna matematička olimpijada, shortlist 1994