Arithmetic and Algebra Session 2 - Difficulty Understanding Solution

[user4727]

Hi there! I’m very new to GregMat and have just started the 1-month study plan. I’m having a difficult time understanding why the solution to the problem below (see screenshot) is only A) 12 and C)36. I understand the minimum value of n is 36, such that n squared = 1296 (which is both divisible by 24 and 108). But can’t the value of n also be 72, such that n squared=5184? 5184 is also divisible by 24 (=216) and by 108 (=48).

In that regard, shouldn’t 72 be included as a divisor of every integer n in S?

Thank you for all the help!!! GregMat has been super useful to me

[cylverixxx]

Correction in one exponent question from problem solving session

“divisors of every integer n”. You correctly identified that n = 36k, for some positive integer k. As such, if n = 36 then 72 is clearly not a divisor of n. In fact, for any odd values k may assume, 72 is not a divisor of n.

I think my answer there also addresses your query.

[user4727]

Ah, got it! Thank you so much!!!