Why does Greg think that n can only have 2^2 because n^2 is 2^3 hence it “gets the job done”?
And why does 3^2 have to be so when n^2 is 3^3?
I don’t understand the logic. Saying n = 2^2 just because n^2 = 2^4 would be able to “get the job done” does not make sense. Same with the logic for the 3.
the question ask for every integer in set S
thus, we can find the LCM of 24 and 108 because it will give us the smallest number that is divisible by both numbers.
LCM\{108,24\} = 216
Prime factorization of 216 = 2^3 \times 3^3
Now, according the question we need to find divisors of every integer n
But here 216 is the LCM of n^2
thus, to find n, n = \sqrt{216} \text{ or } \sqrt{2^3 \times 3^3}
Know we now that n is an integer and hence, we need a even number on it;s prime factor hence we add an additional 2 \text{ and } 3.
n = \sqrt{2^4 \times 3^4}
Solving the square root , n = 2^2 \times 3^2 = 36
Now, only 12 is a divisor of n !
I saw the video a long time ago, so I don’t remember the answer, but following the logic, shouldn’t 36 be also a divisor of n?
