## ABSTRACT

Fermat’s Last Theorem is a special problem in the general theory of Diophantine equations-integer solutions of polynomial equations. To place the problem in context, we move to the wider realm of algebraic numbers, which arise as the real or complex solutions of polynomials with integer coefficients; we focus particularly on algebraic integers, which are solutions of polynomials with integer coefficients where the leading coefficient is 1. For example, the equation x2 − 2 = 0 has no integer solutions, but it has two real solutions, x = ±√2. The leading coefficient of the polynomial x2 − 2 is 1, so ±√2 are algebraic integers.