It generalizes the Cauchy integral theorem and Cauchy's integral formula. Induction yields another proof of the binomial theorem. Suppose the finite Ramsey theorem is false. See also the Weierstrass factorization theorem. This is the fundamental theorem of arithmetic. This is the crux of the Fundamental Theorem of Calculus. Barrow provided the first proof of the fundamental theorem of calculus. Khayyam was the mathematician who noticed the importance of a general binomial theorem. This relies on the Monotone convergence theorem. That situation arises in the context of the circular convolution theorem. See also the less trivial Titchmarsh convolution theorem. By the First Fundamental Theorem of Calculus, formula 74. This is equivalent to the Pythagorean theorem. Assume the function satisfies the hypotheses of the theorem. Several proofs of Fermat's little theorem are known.