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
re: Solution (i think) by Charlie)
That's a fair point. If you start with N which is 0 mod 4, then two operations give you 9N/4. If this is odd, then a third operation makes it 9N/4 + (9N/4)/3 = 12N/4 = 3N. So we reach a number which is still 0 mod 4 with one more factor of 3 than N. So this process still adds factors of 3.
Some starting values of N will take longer to get there than others but I think this shows they'll all get there eventually.
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Posted by tomarken
on 2021-03-18 11:45:56 |
re(2): Solution (i think)
