I wondered if a square minus a square could be a square ? When I put question into equation, I have
aa - bb = cc (when condition is a > b) *I don't know what is the correct notation of a mathematical condition
Q1: Is that right, that we always got a rectangle ?
Q2: Is there some easy way how to prove this ?
Q3: If answer to Q1 is true, is it also true when we remove the condition ?
Update
Q1 does not make sense, because we always get two rectangles, not one. But we can join these two rectangles to composed one. (which can have same square area as some other square)
Restrict to the set of natural numbers.
If $a^2-b^2 = c^2$, then $a^2=b^2+c^2$. The triples $(a,b,c)$ with this property are called Pythagorean triples. There are infinitely many of them.