A triple of natural numbers \(a,b,c\) such that \(a^2 + b^2 = c^2\) is called a Pythagorean triple. There are some small Pythagorean triples that are well-known, like \(3,4,5\) and \(5,12,13\). Let us have a look at the latter one. We can notice an interesting thing: not only \(5^2+12^2=13^2\), but also \(5^2 = 25 = 12+13\) and \(13-12=1\). Use that as an inspiration to find an idea of how to generate some more Pythagorean triples. Check if they are correct by plugging them into the equation \(a^2 +b^2 = c^2\).