The so-called Pythagorean number is three numbers that can form three sides of a right triangle.

Pythagorean Theorem of Right Triangle: C? =a？ +b？

The maximum number is c=2n? +2n+ 1, then

c？ =(2n？ +2n+ 1)？

=(2n？ +2n)？ +2(2n？ +2n)+ 1

=(2n？ +2n)？ +(2n+ 1)？

=b？ +a？

The expressions of the other two numbers are (2n? +2n) and (2n+ 1)