IMO 2011 Shortlist Problem N1

This is a problem that I proposed for IMO 2011. It ended up in the IMO Shortlist, a set of 30 problems selected by the Problem Selection Committee from the 142 proposed problems from around the world. The IMO Jury then deliberated on the IMO Shortlist to select 6 problems for inclusion in the actual IMO paper (I was in the Jury too). Eventually the problem did not make it to the IMO, but I am proud of this nice little problem:

For any integer d > 0, let f(d) be the smallest positive integer that has exactly d positive divisors (so for example we have f(1)=1, f(5)=16, andf(6)=12). Prove that for every integer k \geq 0 the number f\left(2^k\right) divides f\left(2^{k+1}\right).

Source: IMO 2011 Shortlist.

Solution in this file: http://www.imo-official.org/problems/IMO2011SL.pdf

One Response to IMO 2011 Shortlist Problem N1

  1. Khoon Yu says:

    Congratulations Suhaimi! Beautiful problem and beautiful solution. Speaks volume of your passion in math.

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