Some Classical Diophantine Equations

An equation of the form $$a_1x_1 + \cdots + a_n x_n = c,$$ (2.1.1) where a1, a2, …, a n , b are fixed integers, is called a linear Diophantine equation. We assume that n ≥ 1 and that coefficients a1, …, a n are all different from zero.