[math-fun] What is special about 323 and squares?

10 Jul 2017

      The minimal number of squares for rectangles up to longest side 380 is
known.

http://int-e.eu/~bf3/squares/view.html#319,323  needs a minimum of 18
squares.

f(323,319)=18,
f(323,293)=17,
f(323,317)=16,
f(323,283)=16,
f(323,281)=16,

Those are all of the cases up to larger side 380 that need more than 15
squares if the aspect ratio is less than 2.
For 15 squares, add the value 352 as hard.

f(323,X)=15, with X in {256, 271, 277, 307, 313}
f(352,X)=15, with X in {283, 289, 293, 299, 307, 311, 317, 325, 329, 331,
333, 343, 347, 349, 351}

For rectangles needing 14 squares, more than half the values have larger
side 323 or 352.

What is special about 323 (and 352) and squares?

--Ed Pegg Jr