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
Maybe more straightforward by tomarken)
Your method is really nice, but has a slight error in your 3rd paragraph
If N is odd, applying the operation once will make it even. Applying the operation a second time (multiplying by 3/2) will make it odd again, and more specifically will make it divisible by 3. Now its largest divisor is N/3, so applying the operation is equivalent to multiplying by 4/3.
It should begin "If N is odd, but not a multiple of 3,..."
(Two iterations from an odd multiple of 3 will, merely double it.)
The point is correct and much more streamlined. The procedure always gets you to an odd multiple of 3.
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Posted by Jer
on 2021-03-20 12:26:28 |
re: Maybe more straightforward
