determine all composite positive integers n for which it is possible to arrange all divisors of n that are greater than 1 in a circle so that no two adjacent divisors are relatively prime.
Sorry to be difficult, but I still cannot grasp how you can generate 12 or 36 from raising a prime number to a power.
I'm at a loss here.
Could you please show me how you can take a prime number and raise it to a power and come up with 12 or 36? Please.
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I think I see what you are implying:
BOTH p & k MUST be prime numbers:
$\displaystyle n = p^k $
? You are the only one who has said anything about raising a prime to a power. All that is being asked about here are composite positive integers. Bruno J's counter example was specifically to show that you do NOT have to have $\displaystyle p^k$.
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I think I see what you are implying:
BOTH p & k MUST be prime numbers:
$\displaystyle n = p^k $