Is it possible to place 2015 different positive integers around a circle so that for any two adjacent numbers, the smaller integer always divides the larger integer and the ratio of the larger to the smaller is a prime number?

Give reasons for your answer.

If 2015 were any even number this is easily done.
Let a,b,c,etc be primes. 

   1
 /   \
a     b 
ac    bc
acd   bcd
acde  bcde
...   ...
 \    /
 abcde...

Posted by Jer on 2015-09-11 11:47:59