Kummer on Fermat's Theorem

    We return to Z(α), at first for α a cube-root of 1, thus the solution α = cos(2π/3) + i sin(2π/3) of z 2 + z + 1 = 0. We saw that if p is a prime number that leaves the remainder 3 on division by 3, then there is an integer a such that a 2 + a + 1 is divisible by p. We considered the greatest common divisor of a − α and p and discovered that it had to be a… CONTINUE READING