This is one of the most famous puzzles in history: Fermat's Last Theorem.
While (a^2 + b^2 = c^2) works perfectly for right triangles, Pierre de Fermat claimed in 1637 that no three positive integers can satisfy (x^n + y^n = z^n) if (n) is greater than 2.
It remained unproven for 358 years until Andrew Wiles cracked it in 1994 using elliptic curves.