Can every real number be written as a sum of 2 real squares, and if not, how to prove that? And how to prove that not every square of a whole number can be written as a sum of two whole squares? I also read something that doesn't seem right to me: if a and b are rational, c must be irrational (counterexample: 3² + 4² = 5²), does the author mean a rational number that is not whole? And how to prove that? I thank you.