MS = Magic Square(s)
As I keep doing math, my math instincts have improved.
Under math challenge problems I've posted a problem with the title, "An Amazing Discovery" regarding MS being dot multiplied by natural numbers that yield a result that's the same regardless of the row or column. Before I got to the 8 x 8 MS, my gut instinct told me that it exists and it would have a second magic number of 1170 (which I've since established last week - in fact I've found two of those 8 x 8 MS).
It's already been stated that for any 4n order MS (n = 1,2,3,4...), you can interchange the quadrants to make more MS. My math instinct told me that 4n order MS exist for all n = natural number whereby you can dot multiply by the suitable number of natural numbers forwards and backwards on the rows and columns to produce MS with a secondary magic number. So for n = 1, the second magic number is 85 for a 4 x 4 MS and 1170 for the 8 x 8 MS. I contend this can be extended to a 12 x 12, 16 x 16, 20 x 20 ad infinitum.
I will leave this as a puzzle for someone to prove (I don't believe it can be disproven). Furthermore I've only found semi MS whereby the diagonals don't participate with the rows and columns towards producing the desired result. So for 8 x 8 MS and above, can someone produce a MS with a second magic number where all the rows, columns and diagonals do lead up to that second magic number? (again, the one resulting from dot multiplication).