There is some natural number written on the board. An operation is defined as adding to the number its maximal proper divisor. Prove that after some iterations of this operation that we get a number that's divisible by 3²⁰²⁰.

(In reply to Solution (i think) by tomarken)

The only thing I see missing in the proof is the step where, for N mod 4=0, you produce 9N/4, which is a number bigger than N that has 2 more factors of 3 than N did.  What is needed is proof that when this operation results in an odd number, that the process of turning it into an even number does not lose any power of 3, or that assures that any lost power of 3 will be recovered and more.

Posted by Charlie on 2021-03-18 11:30:59