Chapter 6.3, Problem 3SP

In this project. we use the Macburin polynomials for e^xto prove that e is irrational. The proof relies on supposing that e is rational and arriving a a contradiction. Therefore, in the following steps, we suppose e = r/s for some integers r and s where s ≠ 0.

3. Using the results from part 2, show that for each remainder R₀(1), R₁(1), R₂(1), R₃(1), R₄(1), we can find an integer k such that kR_n(1) is an integer for n = 0, 1, 2, 3, 4.