How to find the closest number to 100,000 and less than 100,000 which is a sum of two squares?
Maybe it is possible to find how many sum of square numbers are between 10,000 and 100,000? Are there few?
I know that $(a^2 + b^2)(c^2 + d^2) = (ac + bd)^2 + (ad - bc)^2$ . Or there is some criteria for knowing which number is a sum of squares in How to determine whether a number can be written as a sum of two squares? But, this could be used, I think, when I already have a number to test (or few numbers to test). I would like to avoid spending hours using trial an error on every number less than 100,000 please.