Light House Errors

Apparently every modern web browser contains developer tools to inspect the function of a particular

web page by simply right clicking and selecting the right menu item. I was notified that my pages on

my web site generated an orange level warning about the use of a no longer supported feature called

Storage Type Persistent in java script main. I immediately searched for a solution of which two were

found in a standard search.

Turn off java script detection and turn off X powered HTTP headers.

The java script detection option disappeared and wasn’t an option in September.

The other option shows no signs of working after considerable time for the change.

Since Cloud Flare controls the java script main we must wait until they find a solution.

Magic Squares And Right Triangles (MSART)

While searing for information about a pattern of common differences between three square integers,

I found a book in the library by Martin Gardner with a few chapters about magic squares, which at

first did not seem related, but contained information about right triangles forming these triads. I took

a few notes and moved on to another book.

Later on I generated a list of these square integer triads and they matched perfectly the pattern in the

spreadsheet where a series of a square integers in the columns get subtracted from a sequences of

square integers in the rows. Looking at the magic square from the book, I noticed the odd diagonal

matched one of the triads on the list.

Curious, I examined the remaining numbers in the magic square and after a bit of rearranging found

two more triads. I didn’t take long to figure out how to make more of these semi-magic squares but

none of the magic squares produced this way ever became a fully magic square. I found an explanation

but it wasn’t satisfying.

Checking his sources for a better answer, I found a single page on magic squares with square integers

in a book by Richard Guy on number theory. In the page was another magic square which didn’t have

all square integers, but had perfect diagonals. A little rearrangement revealed more square integer triads

and a completely new way to make a magic square by crossing two triads.

Strangely, the computer results this time revealed no new magic squares with different square integers,

just multiples of the first one ever found. Admittedly, I picked a rather simple looking but not easily

solved problem.