Everyone knows Pythagoras’s theorem: $3^2+4^2=5^2$. There are infinitely many triples of whole numbers like this, such as $5,12,13$ and $8,15,17$. What about cubes? Are there positive integers with $a^3+b^3=c^3$? And with fourth powers? The note in the margin The page of problem II.8 in the 1670 edition of Diophantus’s Arithmetica. Just below the problem comes the “Observatio Domini Petri de Fermat”: the margin note, printed by Fermat’s son.Diophantus, ed. Samuel de Fermat (1670) · Wikimedia Commons · public domain Around 1637, reading Diophantus’s problem about splitting a square into two squares, Fermat wrote in the margin of the book, in Latin: