History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
Fermat's theorem on sums of two squares he announced the following two results for odd primes formula_4: He also wrote: In other words, if "p, q" are of the form 20"k" + 3 or 20"k" + 7, then "pq" = "x" + 5"y". Euler later extended this to the conjecture that Both Fermat's assertion and Euler's conjecture were established by Lagrange. A generalization of Fermat's theorem, the sum of two squares theorem, characterizes the integers (not necessarily prime) that can be expressed as the sum of two squares. They are exactly the integers in which each prime that is congruent to 3 mod 4 appears with an